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

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

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

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

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

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

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

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

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

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Example Prove Theorem 6.6

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Homework Page 342- See assignment guide

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