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Published byChristian Phillips Modified over 4 years ago

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2.6 Proving Statements about Angles

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Properties of Angle Congruence ReflexiveFor any angle, A <A <A. SymmetricIf <A <B, then <B <A. TransitiveIf <A <B and <B <C, then <A <C.

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

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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

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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

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Linear Pair Postulate If two angles form a linear pair, then they are supplementary. 12 m<1 + m<2 = 180°

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

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

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

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

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

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Solve for x.

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

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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.) 1. Given 4. Vertical ’s Theorem 2. Vertical ’s Theorem StatementsReasons 1. 6 7 4. 5 6 2. 7 8 3. 6 8 3. Trans. POC 5. 5 8 5. Trans. POC

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