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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 ….

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Chapter 6 Section 6.3

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  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!! 

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