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8.2 & 8.3 - Properties of Parallelograms

8.2 & 8.3 - Properties of Parallelograms. Parallelogram:. Quadrilateral with both pairs of opposite sides parallel. Theorem: If a quadrilateral is a parallelogram, then both pairs of ___________ sides are ______________. opposite. congruent. Theorem:

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8.2 & 8.3 - Properties of Parallelograms

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  1. 8.2 & 8.3 - Properties of Parallelograms

  2. Parallelogram: Quadrilateral with both pairs of opposite sides parallel

  3. Theorem: If a quadrilateral is a parallelogram, then both pairs of ___________ sides are ______________. opposite congruent

  4. Theorem: If a quadrilateral is a parallelogram, then both pairs of ___________ angles are _____________. congruent opposite

  5. Theorem: If a quadrilateral is a parallelogram, then both pairs of ___________ angles are _____________. consecutive supplementary A B mA + mB = 180° mA + mD = 180° mB + mC = 180° C D mC + mD = 180°

  6. Theorem: If a quadrilateral is a parallelogram, then both diagonals _______________ each other. bisect

  7. 1. Find the value of each variable in the parallelogram. 8 11

  8. 1. Find the value of each variable in the parallelogram. a – 3 = 14 a = 17 b + 2 = 7 b = 5

  9. 1. Find the value of each variable in the parallelogram. g + 7 = 15 g = 8 h – 8 = 12 h = 20

  10. 1. Find the value of each variable in the parallelogram. 3x + 6 = 12 3x = 6 x = 2 2y + 9 = 27 2y = 18 y = 9

  11. 2. Find mB and mC. 119° 61°

  12. 3. Find mJ and mK. 102° 78°

  13. 4. Find the value of each variable in the parallelogram. x + 2 3x = 6 x = 2 3x 6 x + 2 = y – 1 y – 1 2 + 2 = y – 1 4 = y – 1 5 = y

  14. 4. Find the value of each variable in the parallelogram. 9b – 2 = 106 9b = 108 b = 12° 7a – 3 + 106 = 180 7a + 103 = 180 7a = 77 a = 11°

  15. 4. Find the value of each variable in the parallelogram. 5q + 4 = 49 5q = 45 q = 9 2p = 124 p = 62°

  16. 16 HI = _________ Opposite sides 

  17. 8 GH = _________ Diagonals bisect each other

  18. 10 KH = _________ Opposite sides 

  19. 16 HJ = _________ 8 Diagonals bisect each other

  20. 28° KIH = _________ Alternate interior angles

  21. 180 – 84 = 96° JIH = _________ Consecutive angles are supplementary

  22. 84° KJI = _________ Opposite angles are 

  23. 96 – 28 = 68° HKI = _________ 96° Opposite angles are 

  24. congruent parallelogram

  25. congruent parallelogram

  26. supplementary parallelogram

  27. bisect parallelogram

  28. congruent parallel parallelogram

  29. What theorem can you use to show the quadrilateral is a parallelogram? one pair of opposite sides are congruent and parallel

  30. What theorem can you use to show the quadrilateral is a parallelogram? the diagonals bisect each other

  31. What theorem can you use to show the quadrilateral is a parallelogram? both pairs of opposite sides are congruent

  32. What theorem can you use to show the quadrilateral is a parallelogram? both pairs of opposite angles are congruent

  33. Is the quadrilateral a parallelogram? Explain. No, Both pairs of opposite sides are not parallel

  34. Is the quadrilateral a parallelogram? Explain. Yes, Both pairs of opposite sides are congruent

  35. Is the quadrilateral a parallelogram? Explain. No, Not a quadrilateral!

  36. Is the quadrilateral a parallelogram? Explain. No, Opposite sides are not congruent

  37. What additional information is needed in order to prove that quadrilateral ABCD is a parallelogram?

  38. What additional information is needed in order to prove that quadrilateral ABCD is a parallelogram?

  39. What additional information is needed in order to prove that quadrilateral ABCD is a parallelogram?

  40. What additional information is needed in order to prove that quadrilateral ABCD is a parallelogram? mCDA + mDAB = 180° mCDA + mDCB = 180°

  41. What additional information is needed in order to prove that quadrilateral ABCD is a parallelogram? DCB  DAB CDA  CBA

  42. HW Problem 8.2 #34 Ans: –2x + 37 = x – 5 M 4y + 5 N x = 14 –2x + 37 x – 5 4y + 5 = y + 14 y = 3 Q y+ 14 P P = 17 + 17 + 9 + 9 = 52u

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