1. 2.8 Proving Angle Relationships

2. Objectives
Write proofs involving supplementary and complementary angles
Write proofs involving congruent and right angles

3. 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

4. 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

5. 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.

6. Your Turn:
QUILTING The diagram below shows one square for a particular quilt pattern. If
and
is a right angle, find
Answer: 50

7. Example 2: form a linear pair and find If and Supplement Theorem
Subtraction Property
Answer: 14

8. Your Turn:
are complementary angles and
and If
find
Answer: 28

9. Example 3:
In the figure, form a linear pair, and Prove that are congruent.
and
Given: form a linear pair.
Prove:

10. Example 3: Proof: Statements Reasons 1. 1. Given 2.
2. Linear pairs are supplementary. 2.
3. Definition of supplementary angles 3.
4. Subtraction Property 4.
5. Substitution 5.
6. Definition of congruent angles 6.

11. 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.

12. 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. Given 4. 1. 2. 3.
linear pairs.

13. Example 4:
If 1 and 2 are vertical angles and m and m find m1 and m2.
Vertical Angles Theorem 1 2
Definition of congruent angles
m1
m2
Substitution
Add 2d to each side.
Add 32 to each side.
Divide each side by 3.

14. Example 4:
Answer: m1 = 37 and m2 = 37

15. Your Turn: find and If and are vertical angles and and
Answer: mA = 52; mZ = 52

16. Assignment Geometry: Pg. 111 – 113 #6, 16 – 24, 27 - 32
Pre-AP Geometry: Pg. 111 – 113 #6, 16 – 24,