Parallelograms

1
Parallelograms

• 5-1

2
EXAMPLE 1
Use properties of parallelograms
ABCD is a parallelogram by the definition of a
parallelogram. Use Theorem 8.3 to find the value
of x.
Substitute x 4 for AB and 12 for CD.
Subtract 4 from each side.
So, y 65.
3
for Example 1
GUIDED PRACTICE
SOLUTION
So, G 60.
4
for Example 1
GUIDED PRACTICE
SOLUTION
Substitute 18 for JK and y 3 for ML.
Subtract 3 from each side.
Substitute
Divide 2 from each side.
5
EXAMPLE 2
Use properties of parallelograms
SOLUTION
6
Standardized Test Practice
EXAMPLE 3
SOLUTION
7
for Examples 2 and 3
GUIDED PRACTICE
SOLUTION
Substitute
8
for Examples 2 and 3
GUIDED PRACTICE
SOLUTION
By theorem 8.6
2 2
Substitute
4
Add
9
for Examples 2 and 3
GUIDED PRACTICE
SOLUTION
10
for Examples 2 and 3
GUIDED PRACTICE
SOLUTION
70
Substitute
40
Subtract
11
EXAMPLE 2
Identify a parallelogram
The doorway shown is part of a building in
England. Over time, the building has leaned
sideways. Explain how you know that SV
TU.
SOLUTION
By Theorem 8.3, you know that opposite sides of a
parallelogram are congruent. So, SV TU.
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EXAMPLE 3
Use algebra with parallelograms
SOLUTION
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EXAMPLE 3
Use algebra with parallelograms
FN
DN
Set the segment lengths equal.
5x 8
3x
Substitute 5x 8 for FN and 3x for DN.
2x 8
0
Subtract 3x from each side.
2x
8
Add 8 to each side.
x
4
Divide each side by 2.
When x 4,
FN 5(4) 8
12 and DN
3(4)
12.
14
for Examples 2 and 3
GUIDED PRACTICE
What theorem can you use to show that the
quadrilateral is a parallelogram?
15
for Examples 2 and 3
GUIDED PRACTICE
What theorem can you use to show that the
quadrilateral is a parallelogram?
16
for Examples 2 and 3
GUIDED PRACTICE
What theorem can you use to show that the
quadrilateral is a parallelogram?
17
for Examples 2 and 3
GUIDED PRACTICE
SOLUTION
Add 3x to each side
Divide each side by 5
18
EXAMPLE 2
Identify a parallelogram
The doorway shown is part of a building in
England. Over time, the building has leaned
sideways. Explain how you know that SV
TU.
SOLUTION
By Theorem 8.3, you know that opposite sides of a
parallelogram are congruent. So, SV TU.
19
EXAMPLE 3
Use algebra with parallelograms
SOLUTION
20
EXAMPLE 3
Use algebra with parallelograms
FN
DN
Set the segment lengths equal.
5x 8
3x
Substitute 5x 8 for FN and 3x for DN.
2x 8
0
Subtract 3x from each side.
2x
8
Add 8 to each side.
x
4
Divide each side by 2.
When x 4,
FN 5(4) 8
12 and DN
3(4)
12.
21
for Examples 2 and 3
GUIDED PRACTICE
What theorem can you use to show that the
quadrilateral is a parallelogram?
22
for Examples 2 and 3
GUIDED PRACTICE
What theorem can you use to show that the
quadrilateral is a parallelogram?
23
for Examples 2 and 3
GUIDED PRACTICE
What theorem can you use to show that the
quadrilateral is a parallelogram?
24
for Examples 2 and 3
GUIDED PRACTICE
SOLUTION
Add 3x to each side
Divide each side by 5