1 / 16

Showing quadrilaterals are parallelograms

Showing quadrilaterals are parallelograms. Bell Ringer. 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. Example 1. Use Opposite Sides.

baird
Download Presentation

Showing quadrilaterals are parallelograms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Showing quadrilaterals are parallelograms

  2. Bell Ringer

  3. 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. Example 1 Use Opposite Sides

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

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

  6. a. b. c. SOLUTION a. Uis supplementary to Tand V (85° + 95° = 180°). So, by Theorem 6.8, TUVWis a parallelogram. b. Gis supplementary to F (55° + 125° = 180°), but Gis not supplementary to H (55° + 120° ≠ 180°). So, EFGHis not a parallelogram. Tell whether the quadrilateral is a parallelogram. Explain your reasoning. Example 3

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

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

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

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

  11. Now You Try 

  12. Now You Try 

  13. Now You Try 

  14. Now You Try 

  15. Page 320

  16. Complete page 320-321#s 8-24 even only • Home Learning • Page 323 #s 28-34 even only

More Related