1. 8.2 – Use Properties of Parallelograms Goal: You will find angle and side measures in 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 ______________. oppositecongruent

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

5. Theorem: If a quadrilateral is a parallelogram, then both pairs of ___________ angles are _____________. consecutivesupplementary A B C D m  A + m  B = 180° m  A + m  D = 180° m  B + m  C = 180° 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 2y + 9 = 27 2y = 18 3x = 6 x = 2 y = 9

11. 2. Find m  B and m  C. 61°119°

12. 3. Find m  J and m  K. 102° 78°

13. 4. Find the value of each variable in the parallelogram. 3x = 6x + 2 y – 1 3x3x 6 x + 2 = y – 1 x = 2 2 + 2 = y – 1 4 = y – 1 5 = y

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

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

16. HI = _________ 16 Opposite sides 

17. GH = _________ 8 Diagonals bisect each other

18. KH = _________ 10 Opposite sides 

19. HJ = _________ 16 Diagonals bisect each other 8

20.  KIH = _________ 28° Alternate interior angles

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

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

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

24. If opposite sides of a quadrilateral are ________________, then the quadrilateral is a ________________. congruent parallelogram

25. If both pairs of opposite angles are _________________, then the quadrilateral is a _________________. congruent parallelogram

26. If consecutive angles are ________________, then the quadrilateral is a ________________. supplementary parallelogram

27. If the diagonals ____________ each other, then the quadrilateral is a ________________. bisect parallelogram

28. If one pair of opposite sides are ____________ and ____________, then the quadrilateral is a ________________. congruent parallelogram parallel

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?

40. 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. Ans: M N P Q –2x + 37 y + 14 x – 5 4y + 5 –2x + 37 = x – 5 x = 14 4y + 5 = y + 14 y = 3 17 + 17 + 9 + 9 =P = 8.2 #34 52u HW Problem SectionPage #Assignment Spiral 8.2 8.3 517 518-520 526-527 Guided Practice #3-6 3-13 odd, 14, 34 2-6, 8, 15, 17, 19, 21 6-8