2 6 Proving Statements about Angles Properties of

2. 6 Proving Statements about Angles

Properties of Angle Congruence Reflexive For any angle, A <A <A. Symmetric If <A <A. Transitive If <A <B and <B then <A <C. <B, then <B <C,

Right Angle Congruence Theorem • All right angles are congruent. A . X B . C Y . . Z

Congruent Supplements Theorem • If two angles are supplementary to the same angle, then they are congruent – If m<1 + m<2 = 180° and m<2 + m<3 = 180°, then m<1 = m<3 or

Congruent Complements Theorem • If two angles are complementary to the same angle, then the two angles are congruent. – If m<4 + m<5 = 90° and m<5 + m<6 = 90°, then m<4 = m<6 or

Linear Pair Postulate • If two angles form a linear pair, then they are supplementary. 1 2 m<1 + m<2 = 180°

Example: • < 1 and < 2 are a linear pair. If m<1 = 78°, then find m<2.

Vertical Angles Theorem • Vertical angles are congruent. 1 4 2 3

Example <1 and <2 are complementary angles. <1 and <3 are vertical angles. If m<3 = 49°, find m<2.

Proving the Right Angle Congruence Theorem Given: Angle 1 and angle 2 are right angles Prove: Statements Reasons 1. Given 2. Def. of right ’s 3. Trans. POE 4. Def. of ’s

Proving the Vertical Angles Theorem 5 6 7 Given: 5 and 6 are a linear pair. 6 and 7 are a linear pair. Prove: 5 7 Statements 1. 5 and 6 are a linear pair. 6 and 7 are a linear pair. 2. 5 and 6 are supplementary. 6 and 7 are supplementary. Reasons 1. Given 2. Linear Pair Postulate 3. Supplements Theorem

Solve for x.

Give a reason for each step of the proof. Choose from the list of reasons given.

Given: 6 7 Prove: 5 8 Plan for Proof: First show that 5 6 and 7 8. Then use transitivity to show that 5 8. ) Statements Reasons 1. 6 7 1. Given 2. 7 8 2. Vertical ’s Theorem 3. 6 8 3. Trans. POC 4. 5 6 4. Vertical ’s Theorem 5. Trans. POC 5. 5 8