Transcript Measuring Angles Section 1.3

Measuring Angles
Section 1.3
Unit 1
ANGLE MEASURE
• Protractor: Used to measure angles.
– A half-circle with coordinates from 0° to 180°
How to use a protractor:
• 1. Put the center of the protractor at
the vertex.
• 2. Align the protractor so that ray AB
passes through 0 on the protractor.
• 3. Read the measure of the angle (in
degrees) at the point where ray AC
intersects the scale on the protractor
Why isn’t the measure of
the angle 55 degrees
instead of 125 degrees?
Define: Angle Measure
• Most commonly measured in degrees
a
180°
b
0°
Definition: Measure of an
Angle
• Suppose that the vertex, V, of <AVB is placed
on the center point of a half-circle with
coordinates from 0° to 180° so that VA and VB
intersect the half-circle. Let a & b be the
coordinates of the intersections.
• Then, the measure of the angle, written as
<AVB, is a  b or b  a
Use the protractor in the figure to find
the measure of the angles indicated:
• <QPR
• <RPS
• m<QPR +
m<RPS
Congruent Angles
• Congruent if one can be
moved onto the other
so that they match
exactly.
• Tick marks are used to
show which angles are
known to be congruent
• NOTE: Angles are said
to match if their sides
match. The length of
the sides do not matter.
ANGLE CONGRUENCE
POSTULATE
• If 2 angles have the same measure, then
they are congruent.
• If 2 angles are congruent, then they have
the same measure.

• If m<ABC = m<DEF, then ______________
• If <ABC  <DEF, then ________________
ANGLE ADDITION
POSTULATE
• If point S is in the interior of <PQR, then
m<PQS + m<SQR = m<PQR
• GIVEN:
EXAMPLE
– m<EDG = 70°
– m<FDH = 60°
E
F
• FIND:
– m<2
– m<3
– m<1
– m<4
– m<EDJ
1
D
4
G
2
3
H
J
SPECIAL ANGLE PAIRS
• Complementary
Angles:
– 2 angles whose
measures have a sum
of 90°.
– Each angle is called
the complement of
the other.
• Supplementary
Angles:
– 2 angles whose
measures have a sum
of 180°.
– Each angle is called
the supplement of
the other.
EXAMPLE
• Name a
complementary
angle pair and a
supplementary
angle pair in the
figure.
C
D
40°
50°
B
A
E
DEFINITION: LINEAR PAIR
• If the endpoint of
a ray falls on a line
so that two angles
are formed, then
the angles are
known as a Linear
Pair.
1
2
LINEAR PAIR PROPERTY
• If two angles form a
linear pair, then they
are supplementary.
• That means:
m<1 + m<2 = 180°
1
2
EXAMPLE
• GIVEN:
– m<CED = 25°
– <AEB and <BED
form a linear pair
B
• FIND:
C
– m<BEC
– m<AEB
– m<AEC
D
A
E
CLASSIFICATION OF
ANGLES
• Classified according to their measure.
• 3 different types of angles:
– Right angle
– Acute angle
– Obtuse angle
Right Angle
• An angle whose
measure is 90°
• The symbol for a
right angle is a small
square placed at the
vertex of the angle.
Acute Angle
• An angle whose measure is LESS
THAN 90°
Obtuse Angle
• An angle whose measure is GREATER
THAN 90°