 # 2.7 Prove Angle Pair Relationships

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2.7 Prove Angle Pair Relationships

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

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.

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.

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

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.

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

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.

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

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

Example 3: form a linear pair and find If and Supplement Theorem