Transcript Angles - Humble ISD

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Angles
Ray
An object that has one
endpoint and continues
infinitely in ONE
direction.
Angle
An object that has two
rays (called sides) with
a common endpoint
(called the vertex).
Example 1
Name each of the following:
A
B
Sides:_____________________
Vertex:_________
Name:_____________________
C
Interior of an Angle
the space between the
rays that create an
angle.
Exterior 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?
R
Q
S
P
Example 3
A) Name a point in the interior of QPS
R
in EXAMPLE 2.
Q
S
P
B) Name a point in the exterior of QPR
in EXAMPLE 2.
Adjacent
To be next to.
SHARING a side.
Angle Addition Postulate
The sum of two adjacent
angles is equal to the
largest angle.
ANGLE ADDITION POSTULATE:
If R is in the interior of QPS, then
mQPR + mRPS = mQPS.
R
Q
S
If mQPR + mRPS = mQPS,
then R is in the interior of QPS.
P
ANGLE ADDITION POSTULATE:
If R is in the interior of QPS, then
mQPR + mRPS = mQPS.
R
Q
S
If mQPR + mRPS = mQPS,
then R is in the interior of QPS.
P
Example 4
If mPQS = 77 and mPQR = 32, then
find mRQS.
P
R
Q
S
Example 5
If mAOC = 70, mAOB =(x + 10), and mBOC =x,
find:
A
x = __________
B
O
mBOC = _______________
mAOB = _______________
C
Angles can be classified by their measure in
degrees.
If an angle has a degree measure less than
90° it is classified as an
_acute angle__.
If an angle has a degree measure equal to 90°
it is classified as a
__ right angle ____.
Acute Angle
An angle
measuring
less than 90°
Right Angle
An angle whose
measure is
exactly 90°
Obtuse Angle
An angle measuring
greater than 90°
but less than 180°
Straight Angle
An angle
measuring
exactly 180°
For each of the following angles
A) Name it.
B) Tell whether its measure is <90, >90, =90, or = 180.
C) Classify it.
Y
L
125
35
F
I
NAME:_________ OR ______
MEASURE:________
CLASSIFICATION___________
T
C
NAME:_________ OR ______
MEASURE:________
CLASSIFICATION___________
R
T
S
NAME:_________ OR ______
MEASURE:________
CLASSIFICATION___________
N
X
S
NAME:_________ OR ______
MEASURE:________
CLASSIFICATION___________
Congruent
to be the same
shape and
same size.
Angle Bisector
a 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.
W
X
Z
Y
Example 8
FG bisects EFH. Find the value of x.
m EFG = (5x – 10);
E
G
m GFH = (3x + 25)
I
F
H
Example 9
FG bisects EFH. Find the value of x.
m GFH = (3x + 20);
E
G
m EFH = (4x + 80)
I
F
H