Proving Quadrilaterals are Parallelograms - Sec 6.3 GOALS: To prove a quadrilateral is a parallelogram (6 ways to do so!)

Proving Quadrilaterals are Parallelograms A quadrilateral is a parallelogram if: 1. Both pairs of opposite sides are parallel (by the definition)

Proving Quadrilaterals are Parallelograms Theorem 6.6 A quadrilateral is a parallelogram if: 2. Both pairs of opposite sides are congruent

Proving Quadrilaterals are Parallelograms Theorem 6.7 A quadrilateral is a parallelogram if: 3. Both pairs of opposite angles are congruent

Proving Quadrilaterals are Parallelograms Theorem 6.8 A quadrilateral is a parallelogram if: 4. Consecutive angles are supplementary

Proving Quadrilaterals are Parallelograms Theorem 6.9 A quadrilateral is a parallelogram if: 5. Diagonals bisect each other

Proving Quadrilaterals are Parallelograms Theorem 6.10 A quadrilateral is a parallelogram if: 6. One pair of opposite sides are congruent and parallel

Example Decide if you have enough information to determine if the following quadrilaterals are parallelograms. Explain your reasoning.

Example Show that W(-1, 2) X(3, 2) Y (1, -2) and Z(-3, -2) are the vertices of a parallelogram.

Example Prove Theorem 6.6

Homework Page 342- See assignment guide