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.

9. 1. Find the value of each variable in the parallelogram.

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. x + 2 3x = 6 x = 2 3x 6 x + 2 = y – 1 y – 1 2 + 2 = y – 1 4 = y – 1
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.

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

16. HI = _________ 16
Opposite sides 

17. GH = _________ 8
Diagonals bisect each other

18. KH = _________ 10
Opposite sides 

19. HJ = _________ 16 8
Diagonals bisect each other

20. KIH = _________
28°
Alternate interior angles

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

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

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

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
parallel
parallelogram

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

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

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

32. both pairs of opposite angles are congruent
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. mCDA + mDAB = 180° mCDA + mDCB = 180°
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 52u Ans: –2x + 37 = x – 5 M 4y + 5 N x = 14
Section
Page #
Assignment
Spiral
8.2
8.3
517
Guided Practice #3-6
3-13 odd, 14, 34
2-6, 8, 15, 17, 19, 21
6-8
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 = =
52u