Warmup: What is the most precise name based on the markings?

6.3 : Proving a quadrilateral is a parallelogram

4 main ways to prove a quad. is a parallelogram 1.) both pairs of opposite sides are congruent 2.)both pairs of opposite angles are congruent 3.)the diagonals bisect each other 4.)one pair of opposite sides is congruent and parallel

Check with a partner

6.4: special parallelograms Rhombus: 1.) Each diagonal of a rhombus bisects a pair of angles. 2.)The diagonals of a rhombus are perpendicular.

Rectangle 1.) The diagonals of a rectangle are congruent.

converses: If the diagonals of a parallelogram are congruent, it is a rectangle. If the diags. of a parallelogram are perpendicular, it is a rhombus. If a diagonal bisects a pair of angles in a parallelogram, it is a rhombus.

Proof of converse of rhombus diagonals. We are given a parallelogram with a pair of bisected angles. StatementsReasons 1.) m<BAC=m<CEB1.) opp. <‘s are congruent 2.) m<1=m<2=m<3=m<42.) defn. bisect