Slide 1

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 2

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 3

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 4

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 5

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 6

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 7

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 8

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 9

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 10

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 11

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 12

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 13

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 14

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 15

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 16

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 17

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry


Slide 18

1-4 Pairs of Angles

Objectives
a. Identify adjacent, vertical, complementary,
and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a
line.
d. Find the distance between two points
Holt Geometry

1-4 Pairs of Angles

Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem
Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BED
AEB and BED have
• a common vertex, E,
• a common side, EB,
• no common interior points.
• Their noncommon sides, EA and ED, are opposite
rays.
• AEB and BED are adjacent angles and form a
linear pair.
Holt Geometry

1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

AEB and BEC

•
•
•
•

AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

Holt Geometry

1-4 Pairs of Angles
Example 1C: Identifying Angle Pairs

Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.

DEC and AEB

•DEC and AEB share E
• do not have a common side
• DEC and AEB are not adjacent angles.

Holt Geometry

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles

You can find the complement of an angle
that measures x° by subtracting its measure
from 90°, or (90 – x)°.
You can find the supplement of an angle that
measures x° by subtracting its measure
from 180°, or (180 – x)°.

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.

A. complement of F
(90 – x)

90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt Geometry

1-4 Pairs of Angles
Practice 1

mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°

Holt Geometry

1-4 Pairs of Angles
Practice 2
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.

m2 = 47°, m3 = 43°, and m4 =43°.
Holt Geometry

1-4 Pairs of Angles
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.

Holt Geometry

1-4 Pairs of Angles
Practice 1

Name the pairs of
vertical angles.

HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
Holt Geometry

mHML  mJMK  60°.
mHMJ  mLMK  120°.

1-4 Pairs of Angles

Holt Geometry

1-4 Pairs of Angles
Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).

= (–5, 5)

Holt Geometry

1-4 Pairs of Angles
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

Holt Geometry

1-4 Pairs of Angles
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates
equal.

12 = 2 + x
– 2 –2

Multiply both sides by
2.
Simplify.
Subtract.

10 = x

Simplify.

The coordinates of Y are (10, –5).
Holt Geometry

2=7+y
– 7 –7
–5 = y

1-4 Pairs of Angles
Practice 1
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.

The coordinates of T are (4, 3).
Holt Geometry