Transcript Angles Overview

Lesson 1-4
Angles
Lesson 1-4: Angles
1
Angle and Points

An Angle is a figure formed by two rays with a common endpoint,
called the vertex.
ray
vertex

ray
Angles can have points in the interior, in the exterior or on the
angle.
A
E
D
B
C
Points A, B and C are on the angle. D is in the interior and E is in the exterior.
B is the vertex.
Lesson 1-4: Angles
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Naming an angle: (1) Using 3 points
(2) Using 1 point
(3) Using a number – next slide
Using 3 points: vertex must be the middle letter
This angle can be named as ABC or CBA
Using 1 point: using only vertex letter
* Use this method is permitted when the vertex point is the vertex
of one and only one angle.
Since B is the vertex of only this angle, this can
also be called  B .
B
Lesson 1-4: Angles
A
C
3
Naming an Angle - continued
Using a number: A number (without a degree symbol) may be
used as the label or name of the angle. This
A
number is placed in the interior of the angle near
its vertex. The angle to the left can be named
B
2
C
as  2 .
* The “1 letter” name is unacceptable when …
more than one angle has the same vertex point. In this case, use
the three letter name or a number if it is present.
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Example

K is the vertex of more than one angle.
Therefore, there is NO K in this diagram.
There is LKM , PKM , and LKP
There is also 2 and 3 but there is no 5!!!
L
M
2
K
3
Lesson 1-4: Angles
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5
4 Types of Angles
Acute Angle: an angle whose measure is less than 90.
Right Angle: an angle whose measure is exactly 90 .
Obtuse Angle: an angle whose measure is between
90 and 180.
Straight Angle: an angle that is exactly 180 .
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Measuring Angles

Just as we can measure segments, we can also measure angles.

We use units called degrees to measure angles.
•
A circle measures _____
360º
?
•
A (semi) half-circle measures _____
?
•
?
A quarter-circle measures _____
90º
•
One degree is the angle measure of 1/360th of a circle.
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Adding Angles


When you want to add angles, use the notation m1,
meaning the measure of 1.
If you add m1 + m2, what is your result?
m1 + m2 = 58.
A
B
36°
m1 + m2 = mADC also.
22°
Therefore, mADC = 58.
1
C
2
D
Lesson 1-4: Angles
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Angle Addition Postulate
Postulate: The sum of the two smaller angles will always equal
the measure of the larger angle.
Complete:
M
K
m  MRK
____ + m KRW
____ = m  MRW
_____
W
R
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Example: Angle Addition
K is interior to MRW, m  MRK = (3x), m KRW = (x + 6) and
mMRW = 90º. Find mMRK.
First, draw it!
3x + x + 6 = 90
4x + 6 = 90
– 6 = –6
4x = 84
x = 21
K
M
W
3x
x+6
R
Are we done?
mMRK = 3x = 3•21 = 63º
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Angle Bisector
An angle bisector is a ray in the interior of an angle that splits the
angle into two congruent angles.
Example: Since 4   6, UK is an angle bisector.
41° K
5
3
41°
j
4
6
U
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Congruent Angles
Definition: If two angles have the same measure, then they are
congruent.
Congruent angles are marked with the same number of “arcs”.
The symbol for congruence is 
Example:
3
5
3   5.
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Example

Draw your own diagram and answer this question:
If ML is the angle bisector of PMY and mPML = 87,
then find:
mPMY = _______

mLMY = _______


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