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2.8 Proving Angle Relationships
Objectives

Write proofs involving supplementary and
complementary angles

Write proofs involving congruent and right
angles
Postulates and Theorems
Copy all of the postulates and Theorems from
Section 2.8.
Postulates 2.10 and 2.11
Theorems 2.3 thru 2.13
Example 1:
TIME At 4 o’clock, the angle between the
hour and minute hands of a clock is 120º.
If the second hand 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
between the second and hour hands?
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 angle formed by the hour
and minute hands, or
.
Example 1:
By the Angle Addition Postulate, the sum of the two
angles is 120, so the angle between the second and hour
hands is also 60º.
Answer: They are both 60º by the definition of angle
bisector and the Angle Addition Postulate.
Your Turn:
QUILTING The diagram below shows one square for
a particular quilt pattern. If
and
is a right angle, find
Answer: 50
Example 2:
If
and
form a linear pair and
find
Supplement Theorem
Subtraction Property
Answer: 14
Your Turn:
If
and
find
.
Answer: 28
are complementary angles and
Example 3:
In the figure,
Given:
Prove:
and
form a linear pair, and
and
Prove that
are congruent.
form a linear pair.
Example 3:
Proof:
Statements
Reasons
1.
1. Given
2.
2. Linear pairs are
supplementary.
3. Definition of
supplementary angles
3.
4.
4. Subtraction Property
5.
5. Substitution
6.
6. Definition of congruent
angles
Your Turn:
In the figure, NYR and RYA form a linear pair,
AXY and AXZ form a linear pair, and RYA and
AXZ are congruent. Prove that RYN and AXY
are congruent.
Your Turn:
Proof:
Statements
Reasons
1.
1. Given
linear pairs.
2.
2. If two s form a
linear pair, then
they are suppl. s.
3.
3. Given
4.
4.
Example 4:
If 1 and 2 are vertical angles and m1
m2
find m1 and m2.
1
m1
2
Vertical Angles Theorem
m2
Definition of congruent angles
Substitution
Add 2d to each side.
Add 32 to each side.
Divide each side by 3.
and
Example 4:
Answer: m1 = 37 and m2 = 37
Your Turn:
If
and
are vertical angles and
find
and
Answer: mA = 52; mZ = 52
and
Assignment

Geometry:
Pg. 111 – 113 #6, 16 – 24, 27 - 32

Pre-AP Geometry:
Pg. 111 – 113 #6, 16 – 24, 27 - 32