1 / 16

Chapter 6 Section 6.3

Chapter 6 Section 6.3. Proving Quadrilaterals Are Parallelograms. Quick Review. Some Properties of Parallelograms. Definition : A parallelogram is a quadrilateral with both pairs of opposite sides congruent. If a quadrilateral is a parallelogram, then ….

cid
Download Presentation

Chapter 6 Section 6.3

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. Chapter 6Section 6.3 Proving Quadrilaterals Are Parallelograms

  2. Quick Review Some Properties of Parallelograms Definition: A parallelogram is a quadrilateral with both pairs of opposite sides congruent If a quadrilateral is a parallelogram, then … both pairs of opposite sides are congruent both pairs of opposite angles are congruent consecutive angles are supplementary diagonals bisect each other

  3. Proving a Quad is a Parallelogram Theorem Theorem 6.6 If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram Quadrilateral PQRS with both pairs of opposite sides congruent PQRS is a parallelogram

  4. Proving a Quad is a Parallelogram Theorem Theorem 6.7 If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram Quadrilateral PQRS with both pairs of opposite angles congruent PQRS is a parallelogram

  5. Proving a Quad is a Parallelogram Theorem Theorem 6.8 If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram mS + mP = 180 and mS + mR = 180 PQRS is a parallelogram

  6. Proving a Quad is a Parallelogram and Theorem Theorem 6.9 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram PQRS is a parallelogram

  7. Proving a Quad is a Parallelogram and Theorem Theorem 6.10 If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram PQRS is a parallelogram

  8. Proving a Quad is a Parallelogram Yes, one pair of opposite sides congruent and parallel Yes, diagonals bisect each other

  9. Proving a Quad is a Parallelogram Yes, both pairs of opposite sides congruent No, same pair of opposite sides must be parallel and congruent

  10. Proving a Quad is a Parallelogram Yes, could show both pairs of opposite sides are parallel Yes, Consecutive angles are supplementary

  11. Proving a Quad is a Parallelogram Theorem 6.9: Theorem 6.8: mCDA + mDCB = 180 OR mDAB + mABC = 180

  12. Proving a Quad is a Parallelogram For a Quadrilateral to be a parallelogram opposite sides must be congruent x + 2 = y - 1 3x = 6 x = 2 2 + 2 = y – 1 4 = y – 1 5 = y

  13. Proving a Quad is a Parallelogram For a Quadrilateral to be a parallelogram opposite angles must be congruent 3x + 5 = x + 3y 2x = 70 x = 35 3(35) + 5 = 35 + 3y 110 = 35 + 3y 75 = 3y 25 = y

  14. Proving a Quad is a Parallelogram For a Quadrilateral to be a parallelogram diagonals must bisect each other x + y = 5y 3x = 12 x = 4 4 + y = 5y 4 = 4y 1 = y

  15. Use both slope and distance formula to show one pair of opposite side is congruent and parallel • Show that the quadrilateral with vertices A(-1, -2), B(5,3), C(-6,2), and D(0,7) is a parallelogram AB = CD AB // CD

  16. HWPg 342 #’s 9, 10, 12, 17-19 all, & 25-26 Quiz on Thursday!! 

More Related