1. Use properties of parallelograms
EXAMPLE 1
Use properties of parallelograms
ALGEBRA
Find the values of x and y.
ABCD is a parallelogram by the definition of a parallelogram. Use Theorem 8.3 to find the value of x.
AB = CD
Opposite sides of a are .
x + 4 = 12
Substitute x + 4 for AB and 12 for CD.
x = 8
Subtract 4 from each side.
By Theorem 8.4, A C,
or m A = m C.
So, y ° = 65°.
In ABCD, x = 8 and y = 65.
ANSWER

2. GUIDED PRACTICE
for Example 1
Find FG and m G. 1.
8, 60°
ANSWER
Find the values of x and y. 2.
25, 15
ANSWER

3. EXAMPLE 2
Use properties of parallelograms
Desk Lamp
As shown, part of the extending arm of a desk lamp is a parallelogram. The angles of the parallelogram change as the lamp is raised and lowered Find m BCD when m ADC = 110°.
SOLUTION
By Theorem 8.5, the consecutive angle pairs in ABCD are supplementary.
So, m ADC + m BCD = 180°.
Because m ADC = 110°,
m BCD =180° –110° = 70°.

4. EXAMPLE 3
Standardized Test Practice
SOLUTION
By Theorem 8 .6, the diagonals of a parallelogram bisect each other. So, P is the midpoint of diagonals LN and OM . Use the Midpoint Formula. =
Coordinates of midpoint P of OM
4 + 0 2
7 + 0 ,
( ) = 7
( )
The correct answer is A.
ANSWER

5. GUIDED PRACTICE
for Examples 2 and 3
Find the indicated measure in JKLM. NM 3.
m JML 5.
ANSWER 2
ANSWER
70° KM 4.
m KML 6.
ANSWER 4
ANSWER
40°

6. Daily Homework Quiz
1. Find the values of a and b in the parallelogram.
ANSWER
42, 26
2. Find the measure of K in the parallelogram.
ANSWER
116o

7. Daily Homework Quiz
Find the indicated measures in parallelogram ABCD.
3. m BCD
ANSWER
43o
4. If BE = 9, find BD.
ANSWER 18