Download Proving Angle Relationships (Geom) WS pg. 99

NAME ______________________________________________ DATE
2-8
____________ PERIOD _____
Study Guide and Intervention
Proving Angle Relationships
Supplementary and Complementary Angles There are two basic postulates for
working with angles. The Protractor Postulate assigns numbers to angle measures, and the
Angle Addition Postulate relates parts of an angle to the whole angle.
Protractor
Postulate
##$ and a number r between 0 and 180, there is exactly one ray
Given AB
##$, such that the measure
with endpoint A, extending on either side of AB
of the angle formed is r.
Angle Addition
Postulate
R is in the interior of /PQS if and only if
m/PQR 1 m/RQS 5 m/PQS.
P
R
Q
S
The two postulates can be used to prove the following two theorems.
If two angles form a linear pair, then they are supplementary angles.
If /1 and /2 form a linear pair, then m/1 1 m/2 5 180.
D
Complement
Theorem
If the noncommon sides of two adjacent angles form a right angle,
then the angles are complementary angles.
@#$ ⊥ GH
@#$, then m/3 1 m/4 5 90.
If GF
Example 1
2
1
A
B
C
F
J
3
4
G
H
Example 2
If /1 and /2 form a
linear pair and m/2 5 115, find m/1.
If /1 and /2 form a
right angle and m/2 5 20, find m/1.
R
Q
W
2
2 1
M
N
1
S
P
m/1 1 m/2 5 180
m/1 1 115 5 180
m/1 5 65
T
m/1 1 m/2 5 90
m/1 1 20 5 90
m/1 5 70
Suppl. Theorem
Substitution
Subtraction Prop.
Compl. Theorem
Substitution
Subtraction Prop.
Exercises
Find the measure of each numbered angle.
1.
2.
T
P
7
Q
8
8
R
S
m/7 5 5x 1 5,
m/8 5 x 2 5
©
Y
X
Glencoe/McGraw-Hill
U
7 6
Z
5
W
V
m/5 5 5x, m/6 5 4x 1 6,
m/7 5 10x,
m/8 5 12x 2 12
99
3. A
11
13
F
12
H
J
C
m/11 5 11x,
m/12 5 10x 1 10
Glencoe Geometry
Lesson 2-8
Supplement
Theorem