2 ObjectivesWrite proofs involving supplementary and complementary anglesWrite proofs involving congruent and right angles
3 Theorems & PostulatesTheorem 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 & PostulatesPostulate 12 ( Linear Pair Postulate) If 2 angles form a linear pair, then they are supplementaryTheorem 2.6 (Vertical Angles Theorem)Vertical angles are congruent.
5 Example 1:In the figure, form a linear pair, and Prove that are congruent.andGiven: form a linear pair.Prove:
6 Example 1: Proof: Statements Reasons 1. 1 & 4 linear pair; 1. Given1. 1 & 4 linear pair;2. Linear pairs are supplementary.2.3. Definition of supplementary angles3.4. Subtraction Property4.5. Substitution5.6. Definition of congruent angles6.
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. Given220.127.116.11.linear pairs.
9 Example 2:If 1 and 2 are vertical angles and m and m find m1 and m2.Vertical Angles Theorem12Definition of congruent anglesm1m2SubstitutionAdd 2d to each side.Add 32 to each side.Divide each side by 3.