angles
DESCRIPTION
Angles. Angle. An object that has two rays (called sides ) with a common endpoint (called the vertex ). A. B. C. Example 1. Name each of the following: Sides:_____________________ Vertex:_________ Name:_____________________. Interior of an Angle. - PowerPoint PPT PresentationTRANSCRIPT
AngleAngle
An object that has two rays (called sides) with
a common endpoint (called the vertex).
Example 1
Name each of the following:
Sides:_____________________
Vertex:_________
Name:_____________________
A
B
C
Interior of an AngleInterior of an Angle
the space between the rays that create an
angle.
Exterior of an AngleExterior of an Angle
the space that is outside of the rays
Example 2
How does the diagram in EXAMPLE 1 differ from the diagram in this example?
Q
P
R
S
Example 3
A) Name a point in the interior of QPS in EXAMPLE 2.
B) Name a point in the exterior of QPR in EXAMPLE 2.
Q
P
R
S
AdjacentAdjacent
To be next to.
SHARING a side.
Angle Addition PostulateAngle Addition Postulate
The sum of two adjacent angles is equal to the
largest angle.
ANGLE ADDITION POSTULATE:
Q
P
R
S
If R is in the interior of QPS, then mQPR + mRPS = mQPS.
If mQPR + mRPS = mQPS, then R is in the interior of QPS.
ANGLE ADDITION POSTULATE:
Q
P
R
S
If R is in the interior of QPS, then mQPR + mRPS = mQPS.
If mQPR + mRPS = mQPS, then R is in the interior of QPS.
Example 4
If mPQS = 77 and mPQR = 32, then find mRQS.
P
Q
R
S
Example 5
If mAOC = 70, mAOB =(x + 10), and mBOC =x, find:
x = __________
mBOC = _______________
mAOB = _______________
O
A
B
C
Acute AngleAcute Angle
An angle measuring
less than 90°
Right AngleRight Angle
An angle whose measure is exactly 90°
Obtuse AngleObtuse Angle
An angle measuring
greater than 90°
but less than 180°
Straight AngleStraight Angle
An angle measuring
exactly 180°
For each of the following anglesA) Name it.
B) Tell whether its measure is <90, >90, =90, or = 180. C) Classify it.
NAME:_________ OR ______MEASURE:________CLASSIFICATION___________
F
Y
I
NAME:_________ OR ______MEASURE:________CLASSIFICATION___________
T
L
C
NAME:_________ OR ______MEASURE:________CLASSIFICATION___________
T
R
S
NAME:_________ OR ______MEASURE:________CLASSIFICATION___________
N X S
35 125
CongruentCongruent
to be the same shape and same size.
Angle BisectorAngle Bisectora line, ray, or segment
that divides an angle into two congruent angles.
Example 7
If XZ is an angle bisector of WXY, name the two congruent angles that it forms.
WX
Z
Y
Example 8
FG bisects EFH. Find the value of x.
m EFG = (5x – 10); m GFH = (3x + 25)
I F H
EG
Example 9
FG bisects EFH. Find the value of x.
m GFH = (3x + 20); m EFH = (4x + 80)
I F H
EG