1. 2.7 Prove Angle Pair Relationships

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

3. Theorems & Postulates
Theorem 2.3 (Right Angles  Theorem) All right angles are congruent.
Theorem 2.4 (  Supplement Theorem) If 2 angles are supplementary to the same angle (or congruent angles), then they are congruent.
Theorem 2.5 ( Complement Theorem ) If 2 angles are complementary to the same angle (or congruent angles), then they are congruent.

4. Theorems & Postulates
Postulate 12 ( Linear Pair Postulate) If 2 angles form a linear pair, then they are supplementary
Theorem 2.6 (Vertical Angles  Theorem)
Vertical angles are congruent.

5. Example 1:
In the figure, form a linear pair, and Prove that are congruent.
and
Given: form a linear pair.
Prove:

6. Example 1: Proof: Statements Reasons 1.  1 &  4 linear pair;
1. Given 1.
 1 &  4 linear pair;
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.

7. 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.

8. 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.

9. Example 2:
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.

10. Example 2:
Answer: m1 = 37 and m2 = 37

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

12. Example 3: form a linear pair and find If and Supplement Theorem
Subtraction Property
Answer: 14

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

14. Assignment
Geometry: Pg. 127 – 131
#3 - 29, 38, 42, 46