Use properties of parallelograms to solve problems.

1. Parallelograms
The student is able to (I can):
• Prove and apply properties of parallelograms.
• Use properties of parallelograms to solve problems.

2. parallelogramparallelogramparallelogramparallelogram – a quadrilateral with two pairs of parallel
sides.
Therefore, a quadrilateral is a parallelogram if and only if it
has two pairs of parallel sides.
>>
>>
T I
ME
,TI ME TE IM

3. Properties ofProperties ofProperties ofProperties of ParallelogramsParallelogramsParallelogramsParallelograms
If a quadrilateral is a parallelogram, then opposite sides are
congruent.
If a quadrilateral is a parallelogram, then opposite angles are
congruent.
,KI NG GK IN≅ ≅
K
NG
I
>>
>>
K
NG
O
∠K ≅ ∠N, ∠O ≅ ∠G

4. Properties ofProperties ofProperties ofProperties of Parallelograms (cont.)Parallelograms (cont.)Parallelograms (cont.)Parallelograms (cont.)
If a quadrilateral is a parallelogram, then consecutive angles
are supplementary.
If a quadrilateral is a parallelogram, then its diagonals bisect
each other.
1 2
34
>>
>>
T U
NE
S
,TS NS ES US≅ ≅
m 1 m 2 180
m 2 m 3 180
m 3 m 4 180
m 4 m 1 180
∠ + ∠ = °
∠ + ∠ = °
∠ + ∠ = °
∠ + ∠ = °

5. Examples Find the value of the variable:
1. x =
2. x =
3. y =
5x + 3 2x + 15
(3x)°
(x + 84)°
y°

6. Examples Find the value of the variable:
1. x =
2. x =
3. y =
5x + 3 2x + 15
4
(3x)°
(x + 84)°
y°
5x + 3 = 2x + 15
3x = 12
3x = x + 84
2x = 84
42
3(42) = 126°
y = 180 – 126
54

7. Examples Find the value of the variable.
4. x =
y =
16
23
x° y°

8. Examples Find the value of the variables.
4. x = 44
y = 136
16
23
x° y°
−  
=   
= °
1 16
sin
23
44
x
= −
= °
180 44
136
y

9. Examples Find the value of the variable:
5. x =
67°
25
x

10. Examples Find the value of the variable:
5. x =
67°
25
x
°=
=
°
=
25
sin67
25
sin67
27.2
x
x