1. Properties of Parallelograms
Objectives
Prove and apply properties of parallelograms.
Use properties of parallelograms to solve problems.
Holt Geometry

2. Any polygon with four sides is a quadrilateral.
However, some quadrilaterals have special properties. These special quadrilaterals are given their own names.
Helpful Hint
Opposite sides of a quadrilateral do not share a vertex. Opposite angles do not share a side.

3. A Diagonal of a polygon is a segment that joins two nonconsecutive vertices.
Have students find more diagonals
diagonals

4. A quadrilateral with two pairs of parallel sides is a parallelogram.
To write the name of a parallelogram, you use the symbol .

7. Using Properties of Parallelograms
PQRS is a parallelogram. Find the angle measure.
m< R
m< Q Q R
70° P S
m< R = 70 °
To find m< Q
70 ° + m < Q = 180 °
m< Q = 110 °

8. Example 1: Properties of Parallelograms
In CDEF, DE = 74 mm,
DG = 31 mm, and mFCD = 42°. Find CF.
 opp. sides 
CF = 74 mm
Subst. prop

9. Example 2: Properties of Parallelograms
In CDEF, DE = 74 mm,
DG = 31 mm, and mFCD = 42°. Find mEFC.
mEFC + mFCD = 180°
 cons. s supp.
mEFC + 42 = 180
Subst. prop.
mEFC = 138°
- prop.

10. Using properties of parallelograms
FGHJ is a parallelogram. Find the unknown length. JH JK 5 F 5 3 G 3 K J H

11. Example 3: Properties of Parallelograms
In CDEF, DE = 74 mm,
DG = 31 mm, and mFCD = 42°. Find DF.
DF = 2DG
 diags. bisect each other.
DF = 2(31)
Subst. prop
DF = 62
Simplify.

12. Examples
Use the diagram of parallelogram JKLM. Complete the statement. LM K L KN
<KJM N
<LMJ LN MJ J M

13. Properties of Parallelograms
Check It Out! Example 1a
In KLMN, LM = 28 in.,
LN = 26 in., and mLKN = 74°. Find KN.
 opp. sides 
LM = 28 in.
Subst. prop

14. Properties of Parallelograms
In KLMN, LM = 28 in.,
LN = 26 in., and mLKN = 74°. Find mNML.
NML  LKN
 opp. s 
mNML = 74°
Subst. prop.

15. Using Properties of Parallelograms to Find Measures
WXYZ is a parallelogram. Find YZ.
 opp. s 
8a–4 = 6a+10
Subst. prop
2a - 4 = 10
- prop
2a = 14
+ prop
a = 7
YZ = 8a – 4 = 8(7) – 4 = 52

16. Properties of Parallelograms
WXYZ is a parallelogram. Find mZ .
mZ + mW = 180°
 cons. s supp.
(9b+2) + (18b–11) = 180
Subst. prop
27b – 9 = 180
Simplify
27b = 189
+ prop
b = 7
mZ = (9b + 2)° = [9(7) + 2]° = 65°

17. 6.2 Properties of Parallelograms
EFGH is a parallelogram.
Find JG.
 diags. bisect each other.
3w = w + 8
Subst. prop
2w = 8
- prop
w = 4
JG = w + 8 = = 12

18. 1. ABCD is a parallelogram 1. Given
Write a two-column proof.
Given: ABCD is a parallelogram.
Prove: ∆AEB  ∆CED
Statements
Reasons
1. ABCD is a parallelogram
1. Given
 opp. sides 
 diags. bisect
each other
4. SSS

19. Write a two-column proof.
Given: RSTU is a parallelogram.
Prove: ∆RSU  ∆TUS
Statements
Reasons
1. RSTU is a parallelogram.
4. ∆RSU  ∆TUS
3. R  T