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Warm Up

Complete each statement about parallelogram ABCD. Warm Up. B. A. G. C. D. Section 8.3 (a) Show that a Quadrilateral is a Parallelogram. Quadrilateral. Both pairs of opposite sides are parallel. Parallelogram. Opposite sides are congruent. Opposite angles are congruent.

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Warm Up

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  1. Complete each statement about parallelogram ABCD. Warm Up B A G C D

  2. Section 8.3 (a)Show that a Quadrilateral is a Parallelogram

  3. Quadrilateral • Both pairs of opposite sides are parallel Parallelogram • Opposite sides are congruent • Opposite angles are congruent • Diagonals bisect each other • Consecutive angles are supplementary

  4. Examples Discussion Solve for the missing variable in the parallelogram. x X = 31 y = 60 y x 13 31 120 y X = 13 Y = 17 17

  5. How do you know if you have a parallelogram? If you have a quadrilateral By definition if both pairs of opposite sides are parallel then it’s a parallelogram.

  6. Is this is parallelogram? How do you know for sure?

  7. Is this is parallelogram? How do you know for sure?

  8. Is this is parallelogram? How do you know for sure?

  9. Given: AB ≅ CD, AD ≅ CB. • Prove: ABCD is a parallelogram. Statement Reason • 1. Given • 1. AB ≅ CD, AD ≅ CB. • 2. Reflexive Prop. of Congruence • 2. AC ≅ AC • 3. ∆ABC ≅ ∆CDA • 3. SSS Congruence Postulate • 4. BAC ≅ DCA, DAC ≅ BCA • 4. Def. of congruence • 5. AB║CD, AD ║CB. • 5. Alternate Interior s Converse • 6. ABCD is a  • 6. Def. of a parallelogram.

  10. 6 ways to show a quadrilateral is a parallelogram 1.Both pairs of opposite sides are parallel 2.Both pairs of opposite sides are congruent 3.Both pairs of opposite angles are congruent

  11. 6 ways to show a quadrilateral is a parallelogram x° y° y° x° x°+y°=180° 4.Consecutive angles are supplementary 5.diagonals bisect each other 6. ONE pair of opposite sides are CONGRUENT & PARALLEL

  12. New Theorem • Theorem 8.9: If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram. B C If BC ║AD and BC ≅ AD, then ABCD is a parallelogram. A D

  13. Examples For what value of x and y is the quadrilateral a parallelogram? 4y 6x - 12 2x + 36 114° y+16° 6y - 42 x°

  14. Examples For what value of x and y is the quadrilateral a parallelogram? R R S S 2y + 12 x 100° T 10 y° 5y 5x - 28 40° Q Q P P 25 x°

  15. Homeworktextbookp.518 #’s 3-15 oddp. 8-10

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