Section 6 3 Notes Tests for Parallelograms EQ

Section 6. 3 Notes: Tests for Parallelograms EQ: How can you prove that a parallelogram is a quadrilateral?

Vocab! Parallelogram Opposite Sides Converse A D B C A Parallelogram Opposite Angles Converse D B C

Example 2 •

You Try! 1. Determine whether the quadrilateral is a parallelogram. Justify your answer. Yes, the quadrilateral is a parallelogram because both pairs of opposite sides are congruent. 2. Which theorem would prove the quadrilateral is a parallelogram? Parallelogram Opposite Sides Converse

Vocab! A Opposite Sides parallel and congruent Theorem Parallelogram Diagonals Converse D B D C A B C

Example 2 For what value of x is quadrilateral CDEF a parallelogram?

Example 3 For what values of x and y is quadrilateral ABCD a parallelogram? Explain your reasoning.

You Try! 1. Find x and y so that the quadrilateral is a parallelogram. 2. Find m so that the quadrilateral is a parallelogram. Opposite Sides parallel and Congruent Theorem 4 m + 2 = 3 m + 8 m = 6 3. For what value of x is quadrilateral MNPQ a parallelogram? Explain your reasoning. Parallelogram Diagonals Converse 2 x = 10 – 3 x x = 2

Example Stating Theorem to Show that a Quadrilateral is a Parallelogram Example 4: Opposite Sides are parallel and congruent Example 5: Parallelogram Opposite Sides Converse Example 6: Parallelogram Opposite Angles Theorem

Show that… • Both pairs of opp. sides are || • Both pairs of opp. sides are ≅ How to Prove • Both pairs of opp. ∠’s are ≅ that a • Diagonals bisect each other Quadrilateral is a • Pair of opp. Sides is both || and ≅ Parallelogram

Example 4 Quadrilateral QRST has vertices Q(– 1, 3), R(3, 1), S(2, – 3), and T(– 2, – 1). Determine whether the quadrilateral is a parallelogram. Justify your answer by using the Slope Formula. If opp. Sides are || then QRST is a parallelogram

Example 5 Graph quadrilateral EFGH with vertices E(-2, 2), F(2, 0), G(1, 5), and H(-3, -2). Determine whether the quadrilateral is a parallelogram. G E F H