Quadrilaterals Worksheet With Answers Page 48
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50We will apply the previous theorem in the following examples.
1. Given: Trapezoid TRAP
P
A
Median MN
TR = (3x – 4) cm
M
N
AP = (x + 2) cm
MN = 15 cm
T
R
Find:
x and TR
x = _________
TR = _________
2. Given: Trapezoid TRAP in example 1
Median MN
m∠PMN = (10x – 27)
m∠PTR = (3x + 29)
Find: x and m∠PTR
Solutions:
1
(The median of a trapezoid has a length
1. MN =
(AP + TR)
2
equal to one-half the sum of the lengths of
the two bases.)
1
15 =
(x + 2 + 3x – 4))
(Substitution)
2
30 = ( x + 2 + 3x - 4)
(Multiplication property of equality)
30 = 4x – 2
32 = 4x
8 = x
TR = 3•8 – 4 = 24 – 4 = 20 cm
2. MN
TR
(The median of a trapezoid is parallel to both
bases.)
m∠PMN = m∠PTR
(If two parallel lines are cut by a transversal,
then the corresponding angles are congruent.)
10x – 27 = 3x +29
(Substitution)
7x = 56
x = 8
m∠PTR = 3•8 + 29 = 24 + 29 = 53
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