Page 200 - Math Course 2 (Book 2)

Proving Angle Relationships
Mo. 12

Lesson 7 THEOREMS

Supplement Theorem

KEY CONCEPTS:
12.3 If two angles form a linear pair, then they
1. Write proofs involving supplementary and are supplementary angles.
complementary angles.
2. Write proofs involving congruent and right
angles.

1 2
MO. 12 - L8a m∠1 + m∠2 = 180

Supplementary and Complement Theorem
Complementary Angles If the noncommon sides of two adjacent

12.4 angles form a right angle, then the angles
are complementary angles.
POSTULATES

Protractor Postulate 1

12.10 Given AB and a number r between 0 and 2
180, there is exactly one ray with endpoints

A, extending on either side of AB, such that m∠1 + m∠2 = 90
the measure of the angle formed is r.

Let’s Begin

B
Angle Addition
A
Angle Addition Postulate
Example
12.11 If R is in the interior of ∠PQS, then
m∠PQR + m∠RQS = m∠PQS.
TIME
If m∠PQR + m∠RQS = m∠PQS, then R is in At 4 o’clock, the angle between the hour and min-
the interior of ∠PQS. ute hands of a clock is 120º. If the second hand
P stops where it bisects the angle between the hour
and minute hands, what are the measures of the
angles between the minute and second hands and
R
Q between the second and hour hands?
S If the second hand stops where the angle is
bisected, then the angle between the minute and
second hands is one-half the measure of the an-
gle formed by the hour and minute hands, or
1
2 (120) = 60

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