9.2 Parallelograms

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. parallelogram parallelogram parallelogram parallelogram –a quadrilateral with two pairs of pa rallel
sides.
Therefore, a quadrilateral is a parallelogram if an d only if it
has two pairs of parallel sides.
>>
>>
TI
M E
T T
 ,
TI ME TE IM

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

4. Properties of Properties of Properties of Properties of Parallelograms (cont.) Parallelograms (cont.) Parallelograms (cont.) Parallelograms (cont.)
If a quadrilateral is a parallelogram, then consecu tive angles
are supplementary.
If a quadrilateral is a parallelogram, then its dia gonals bisect
each other.
1 2
3 4
>>
>>
TU
N E
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+ 32x+ 15
(3x)°
(x+ 84)°
y°

6. Examples
Find the value of the variable:
1.x=
2.x=
3.y=
5x+ 32x+ 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