1. 1.
Find the value of x.
ANSWER 60 2.
Find the coordinates of the midpoint of AB with endpoints A(–2, 6) and B(10, 4).
ANSWER
(4, 5) 3.
Find the distance between (–2, 6) and (10, 4).
ANSWER 37 2

2. Use properties of parallelograms.
Target
Use properties of parallelograms.
You will…
Find angle and side measures in parallelograms.

3. Vocabulary
parallelogram – a quadrilateral with both pairs of opposite
sides parallel
Properties of Parallelograms
If a quadrilateral is a parallelogram, then
opposite sides are congruent – Theorem 8.3
opposite angles are congruent – Theorem 8.4
consecutive angles are supplementary – Theorem 8.5
diagonals bisect each other – Theorem 8.6.

4. 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 and Theorem 8.4 to find the value of y.
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

5. 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

6. 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°.

7. 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

8. 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°