1. Showing quadrilaterals are parallelograms

2. Bell Ringer

3. Use Opposite Sides Example 1 Tell whether the quadrilateral is a parallelogram. Explain your reasoning. SOLUTION The quadrilateral is not a parallelogram. It has two pairs of congruent sides, but opposite sides are not congruent.

4. Use Opposite Angles Example 2 SOLUTION The quadrilateral is a parallelogram because both pairs of opposite angles are congruent. Tell whether the quadrilateral is a parallelogram. Explain your reasoning.

5. Now You Try Tell whether the quadrilateral is a parallelogram. Explain your reasoning. 1. In quadrilateral WXYZ, WX = 15, YZ = 20, XY = 15, and ZW = 20. Is WXYZ a parallelogram? Explain your reasoning. 3. 2. ANSWER Yes; both pairs of opposite sides are congruent. No; opposite angles are not congruent. ANSWER No; opposite sides are not congruent.

6. Example 3 Tell whether the quadrilateral is a parallelogram. Explain your reasoning. a. b.c. SOLUTION  U is supplementary to  T and  V (85° + 95° = 180°). So, by Theorem 6.8, TUVW is a parallelogram. a.  G is supplementary to  F (55° + 125° = 180°), but  G is not supplementary to  H (55° + 120° ≠ 180°). So, EFGH is not a parallelogram. b.

7. Use Consecutive Angles Example 3  D is supplementary to  C (90° + 90° = 180°), but you are not given any information about  A or  B. Therefore, you cannot conclude that ABCD is a parallelogram. c.

8. Example 4 Tell whether the quadrilateral is a parallelogram. Explain your reasoning. b. SOLUTION a. The diagonals of JKLM bisect each other. So, by Theorem 6.9, JKLM is a parallelogram. a. The diagonals of PQRS do not bisect each other. So, PQRS is not a parallelogram. b.

9. Now You Try 4. 5. ANSWER No; opposite angles are not congruent (or consecutive angles are not supplementary). Yes; one angle is supplementary to both of its consecutive angles. ANSWER Tell whether the quadrilateral is a parallelogram. Explain your reasoning.

10. Now You Try ANSWER Yes; the diagonals bisect each other. No; the diagonals do not bisect each other. ANSWER 7. 6. Tell whether the quadrilateral is a parallelogram. Explain your reasoning.

11. Now You Try

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