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. SOLUTION FG = HE x =
Opposite sides of a are .
x = 8
By Theorem 8.4, E G,
or m E = m G.
So, G ° = 60°.
In FEHG, FG = 8 and m G = 60°.
ANSWER

3. Find the values of x and y. 2.
GUIDED PRACTICE
for Example 1
Find the values of x and y. 2.
SOLUTION
JK = ML
Opposite sides of a are .
18 =
y + 3
Substitute 18 for JK and y + 3 for ML.
15 = y
Subtract 3 from each side.
By Theorem 8.4, J L,
or m J = m L.
2x = 50
Substitute
x = 25
Divide 2 from each side.
In JKLM, x = 25 and y = 15.
ANSWER