Parallelogram

**//Parallelogram//** is a @trapezoid with 2 pairs of parallel sides
 * __Definition__ **

//Side Properties// 1. ** Opposite sides are congruent
 * __ Properties __**

** //Angle Properties// **** 1. ** Opposite angles are congruent  Prove: Angle APE is congruent to Angle ARE Angle PAR is congruent to Angle PER 
 * Example Proof**

**Example Proof** Prove: Angle ARG and Angle ARE are supplementary
 * 2. ** Consecutive angles are supplementary

** //Diagonal Properties// ** ** 1. ** Diagonals bisect each other Segment AE bisects Segment PR Segment LA is congruent to Segment LE

Segment PR bisects Segment AE Segment LP is congruent to Segment LR

** 2. * ** Oppositely oriented triangles formed by diagonals are congruent **Example Proof** Prove: Triangle RAT is congruent to Triangle CAE

This property is the most important of a parallelogram for the following reasons: - Knowing that opposite triangle pairs are congruent, the congruence of their corresponding sides and angles can be proved by CPCTC. Such information can help find side and angle measurements