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2.7 Prove Angle Pair Relationships

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.

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2.7 Prove Angle Pair Relationships

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

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

  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 AXYare congruent.

  8. 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. Your Turn:

  9. If 1 and 2are vertical angles and m1 andm2 find m1 and m2. 1 2 Vertical Angles Theorem m1 m2 Definition of congruent angles Example 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. If and are vertical angles and and find and Your Turn: Answer: mA= 52; mZ= 52

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

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

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

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