EXPLAIN 1 Proving Opposite Sides Are Congruent Read the section below and complete the following activity adapted from Lesson 9 1 A segment that connects two nonconsecutive vertices of a polygon is a diagonal 6 Theorem 1 If a quadrilateral is a parallelogram then its opposite sides are congruent Example reason box at the bottom of page Prove that the opposite sides of a parallelogram are congruent Answers given in statement Given ABCD is a parallelogram Prove AB CD and AD CB The figure WXYZ is a parallelogram WZ XY and WX ZY Statements 3 AB DC AD BC 4 ZADB ZCBD LABD LCDB 5 DB DB 1 ABCD is a parallelogram 2 Draw DB 7 AB CD and AD CB Statement Reason Bank 3 1 2 Through any two points there is exactly one line 4 D 5 Reasons 6 ASA Triangle Congruence Theorem 7 4 Alternate Interior 1 Given Angles Theorem 5 Reflexive Property of Congruence 7 CPCTC This number tells you the correct row number in the proof for each statement or reason provided below 3 Definition of parallelogram 6 A ABDA CDB 0