Warm Up 6.3 on desk Do daily Quiz 6.2

6.3 Essential Objective: Essential Question: Show that a quadrilateral is a parallelogram. Essential Question: How do we prove that a quadrilateral is a parallelogram?

Theorem 6.6 If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Tell whether the quadrilateral is Example 1 Use Opposite Sides Tell whether the quadrilateral is a parallelogram. Explain your reasoning. SOLUTION The quadrilateral is not a parallelogram.

Example 2 Use Opposite Angles Tell whether the quadrilateral is a parallelogram. Explain your reasoning. SOLUTION The quadrilateral is a parallelogram

Checkpoint Use Opposite Sides and Opposite Angles In Exercises 1 and 2, tell whether the quadrilateral is a parallelogram. Explain your reasoning. 1. 2.

Opposite sides are congruent. Checkpoint Use Opposite Sides and Opposite Angles In Exercises 1 and 2, tell whether the quadrilateral is a parallelogram. Explain your reasoning. 1. ANSWER Yes; both pairs of Opposite sides are congruent. 2. No; opposite angles Are not congruent. ANSWER 7

Theorem 6.8 If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

Example 3 Use Consecutive Angles Tell whether the quadrilateral is a parallelogram. Explain your reasoning. a. b. c. 9

Theorem 6.9 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Example 4 Use Diagonals Tell whether the quadrilateral is a parallelogram. Explain your reasoning. a. b. 11

No; opposite angles are not congruent (or consecutive angles are Checkpoint Use Consecutive Angles and Diagonals Tell whether the quadrilateral is a parallelogram. Explain your reasoning. c. ANSWER No; opposite angles are not congruent (or consecutive angles are not supplementary). d. Yes; one angle is supplementary to both of its consecutive angles. ANSWER 12

Yes; the diagonals bisect each other. Checkpoint Use Consecutive Angles and Diagonals Tell whether the quadrilateral is a parallelogram. Explain your reasoning. e. ANSWER Yes; the diagonals bisect each other. f. No; the diagonals do not bisect each other. ANSWER 13

Homework