Name:__________________________________
Date:____________
Properties of Trapezoids
I. For each trapezoid or triangle, find the measure of each angle or the length of each segment. The dashed segments are
medians.
16
A
1.
B
N
2.
R
118°
M
10
E
49°
16
F
8
11
75°
C
D
Q
30
m D _________
m
 FED ______
AE _________
P
S
m  B________
m
 N ______ m  M _________
EF _________
m
 P ______
RS _________
BC _________
T
S
F
3.
G
4.
126°
26
L
K
6
73°
W
J
V
m
 S_______
m
 T _______
m
 W _______
m
 G _______
FL __________
G 2
m
H
 H ________
FG __________
C
5.
61°
D
1
B
A
21
2
34
E
m
 A ______
m  1 ________
m
 E _______
m  2 _______
BD ___________
6. The measure of one angle of an isosceles trapezoid is 155°. Find the measures of the other three angles.
7. The median of a trapezoid measures 18 cm and is 11 cm longer than one of the parallel sides. How
long is the other parallel side?
1
II. Find the missing segment if ST is the median of trapezoid UVWX.
U
8. XW = 6, ST =4, UV =
V
9. UV = 13, ST = 20, XW =
T
S
10. XW = 10, ST = 12, UV =
11. UV = 9.3, XW = 6.7, ST =
X
W
12. XW= 6, UV = 12, ST =
13. ST = 18, XW = 7, UV =
III. Find the value of x or y if ST is the median of trapezoid UVWX.
U
V
14. UV = 6y, XW = 14y, ST = y + 18.
T
S
Equation:
X
W
y=
15. UV = 10y + 2, XW = 6y, ST = 3y + 21.
U
V
Equation:
S
X
T
W
y=
2
16. XW = 4x, VU = 7x, TS = 22
U
Equation:
V
S
T
X
W
x=
U
17. XW = 2x + 5, VU = 3x + 6, ST = 33
Equation:
V
S
T
X
W
x=
IV. Solve assuming trapezoid UVWX is isosceles.
18.
U = 119°
 W = 61°
 V = 3x – 4y
 X = 2x + y
U
S
V
T
Equation 1 :
Equation 2 :
x = ______
X
W
y = ______
3
19. m  U = x2 – 8x
m  X = 160°
U
V
Equation:
T
S
X
x=
W
or
20. m  X = x2 + 72
m  W= 17x
U
V
Equation:
S
X
x=
T
W
or
4