EXPLAIN 2 Proving Opposite Angles Are Congruent Read the section below and complete the following activity (adapted from Lesson 9.1). Theorem 2 If a quadrilateral is a parallelogram, then its opposite angles are congruent. The Agure WXYZ is a parallelogram. ZZWXLXYZ and ZWZY ZWXY W Example Prove that the opposite angles of a parallelogram are congruent. Given: ABCD is a parallelogram. Prove: ZAZC (A similar proof shows that ZBZD.) D Statements 1. ABCD is a parallelogram. 1. 2. Draw DB. 2. 3. AB||DC, AD||BC 3. 4. 5. 6. 7. Reasons 4. Alternate Interior Angles Theorem 5. Reflexive Property of Congruence 6. ASA Triangle Congruence Theorem 7. B Statement & Reason Bank 1 Given 7S ALC 4 ZADB LCBD, LABD LCDB 2 Through any two 7R CPCTC 5 DB DB points, there is exactly one line. 6 AABDA CDB 3 Definition of parallelogram