1 / 19

QUADRILATERALS

QUADRILATERALS. A Study of all things 4 sided. Parallelograms. Definition: A quadrilateral with both pairs of opposite sides parallel. Properties of Parallelograms. Theorems and Conclusions. Theorem # 28 :

marty
Download Presentation

QUADRILATERALS

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. QUADRILATERALS A Study of all things 4 sided

  2. Parallelograms

  3. Definition: • A quadrilateral with bothpairs of opposite sides parallel.

  4. Properties of Parallelograms Theorems and Conclusions

  5. Theorem # 28: • If a quadrilateral is a parallelogram, then the pairs of opposite sides are congruent. Parallelograms Both pairs of opposite sides parallel Both pairs of opposite sides congruent.

  6. Theorem # 29: • If a quadrilateral is a parallelogram, then both pairs of opposite angles are congruent. Parallelograms Both pairs of opposite sides parallel Both pairs of opposite sides congruent Both pairs of opposite angles congruent

  7. Theorem # 30: • If a quadrilateral is a parallelogram, then the pairs of consecutive angles are supplementary. Parallelograms Both pairs of opposite sides parallel Both pairs of opposite sides congruent Both pairs of opposite angles congruent Pairs of consecutive angles are supplementary 4 1 2 3

  8. Theorem # 31: • If a quadrilateral is a parallelogram, then the diagonals bisect each other. Parallelograms Both pairs of opposite sides parallel Both pairs of opposite sides congruent Both pairs of opposite angles congruent Pairs of consecutive angles are supplementary Diagonals bisect each other

  9. Example #1: • Name any pairs of parallel sides. • Name any pairs of congruent segments. • Name any pairs of congruent angles. • Name any pairs of supplementary angles. Answers: B C E A D

  10. Parallelogram “HOT FACTS” • 4 Sides – Quadrilateral • 2 pairs of opposite sides parallel • 2 pairs of opposite sides congruent • 2 pairs of opposite angles congruent • 4 pairs of consecutive angles supplementary • Diagonals bisect each other

  11. Proving Quadrilaterals are Parallelograms Are you sure they’re parallelograms?

  12. Theorem # 32: • If a quadrilateral has both pairs of opposite sides congruent, then the quadrilateral is a parallelogram. Parallelograms BOTH pairs of opposite sides congruent parallelogram

  13. Theorem # 33: • If a quadrilateral has both pairs of opposite angles congruent, then the quadrilateral is a parallelogram. Parallelograms BOTH pairs of opposite sides congruent parallelogram BOTH pairs of opposite angles congruent parallelogram

  14. Theorem # 34: • If a quadrilateral has a pair of consecutive angles supplementary, then the quadrilateral is a parallelogram. Parallelograms BOTH pairs of opposite sides congruent parallelogram BOTH pairs of opposite angles congruent parallelogram A pair of consecutive angles supplementary parallelogram 4 1 2 3

  15. Theorem # 35: • If a quadrilateral’s diagonals bisect each other, then the quadrilateral is a parallelogram. Parallelograms BOTH pairs of opposite sides congruent parallelogram BOTH pairs of opposite angles congruent parallelogram A pair of consecutive angles supplementary parallelogram Diagonals bisect each other parallelogram

  16. Theorem # 36: • If a quadrilateral has exactly 1 pair of opposite sides congruent and parallel, then the quadrilateral is a parallelogram. Parallelograms BOTH pairs of opposite sides congruent parallelogram BOTH pairs of opposite angles congruent parallelogram A pair of consecutive angles supplementary parallelogram Diagonals bisect each other parallelogram Exactly 1 pair of opposite sides congruent and parallel parallelogram

  17. Definition: • A quadrilateral with bothpairs of opposite sides parallel. Parallelograms Both pair of opposite sides parallel  parallelogram

  18. Area of a Parallelogram • Area = base * height • A = b * h h b

  19. Everything you ever wanted to know about Parallelograms…You now know If you did things right, you should have only used 1 sheet of paper, right?

More Related