EXPLAIN 2 Proving Opposite Angles Are Congruent Read the section below and complete the following activity adapted from Lesson 9

Question

EXPLAIN 2 Proving Opposite Angles Are Congruent Read the section below and complete the following activity adapted from Lesson 9 1 Example Prove that the opposite angles of a parallelogram are congruent Given ABCD is a parallelogram Prove ZA ZC A similar proof shows that ZB ZD 5 Theorem 2 If a quadrilateral is a parallelogram then its opposite angles are congruent The gure WXYZ is a parallelogram 2ZWX 2XYZ and ZWZY ZWXY 1 ABCD is a parallelogram 2 Draw DB 6 3 AB DC AD BC 4 7 Statements Statement Reason Bank 1 2 6 3 1 Given D Reasons 4 Alternate Interior Angles Theorem 5 Reflexive Property of Congruence 6 ASA Triangle Congruence Theorem 7 A ABD A CDB 2 Through any two 7R CPCTC points there is exactly one line W 7S LA LC B 4 LADB LCBD LABD LCDB 5 DB DB 3 Definition of parallelogram

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