1. Properties of Parallelograms
6-2
Properties of Parallelograms
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry
Holt Geometry

2. Warm up:
x=360
247+x=360
x=113
2x x-1+8x=360
13x+165=360
13x=195
x=15

3. Objectives
Use properties of parallelograms to solve problems.

4. Any polygon with four sides is a _______________.
However, some quadrilaterals have special properties. These special quadrilaterals are given their own names. For example….
A parallelogram is
To write the name of a parallelogram, you use the symbol
quadrilateral
a quadrilateral with both pairs of opposite sides being parallel.

6. Properties of parallelograms
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.

7. a. FGHJ is a parallelogram. Find JH and FJ.5 3

8. b. ABCD is a parallelogram. Find AB and AD.8 9

9. c. PQRS is a parallelogram. Find the missing angle measures.70
110
110

10. d. ABCD is a parallelogram. Find the missing angle measures.
120
120 60

11. e. TUVW is a parallelogram. Find TX.3

12.
y=98
2x=4
x=12
x=2
180-98=x
3y+1=10
y-1=6
x=82
3y=9
y=7
y=3

13. Example 7
EFGH is a parallelogram.
Find JG.
 diags. bisect each other.
3w = w + 8
Substitute.
2w = 8
Simplify.
w = 4
Divide both sides by 2.
JG = w + 8 = = 12

14. Exmaple 8
EFGH is a parallelogram.
Find FH.
 diags. bisect each other.
4z – 9 = 2z
Substitute.
2z = 9
Simplify.
z = 4.5
Divide both sides by 2.
FH = (4z – 9) + (2z) = 4(4.5) – 9 + 2(4.5) = 18

15. Example 9
WXYZ is a parallelogram. Find YZ.
 opp. sides 
8a – 4 = 6a + 10
Substitute the given values.
Subtract 6a from both sides and add 4 to both sides.
2a = 14
a = 7
Divide both sides by 2.
YZ = 8a – 4 = 8(7) – 4 = 52

16. Example 10
WXYZ is a parallelogram. Find mZ .
mZ + mW = 180°
 cons. s supp.
(9b + 2) + (18b – 11) = 180
Substitute the given values.
27b – 9 = 180
Combine like terms.
27b = 189
Add 9 to both sides.
b = 7
Divide by 27.
mZ = (9b + 2)° = [9(7) + 2]° = 65°

17. QRST is a parallelogram. Find each measure.
11. TQ

18. 12. mS

19. 12. MR