PreAP Geometry
Name__________________________
Review for Test #3- Quadrilaterals
The figures are NOT drawn to scale. In fact, the figures can be misleading. So use what you know about the properties of
each quadrilateral to help you complete each problem.
ABCD is a rectangle. Find m1 , m2 , m3 ,
AC , and DC .
1.
A
ABCD is a rhombus with BD  8 . Find m1 ,
m2 , m3 , AE , and AC .
2.
B
5
A
1
D
3
E
2
8
E
1
30°
ABCD is a square. Find m1 , m2 , m3 , BC ,
AC , and ED .
12
A
ABCD is an isosceles trapezoid with AB DC . Find
x , m1 , and m2 .
15
A
B
1
12
E
3
D
C
4.
B
2
1
3
D
C
3.
III.
B
37°
2
2
30°
C
D
70°
x2-x
E
40°
22
C
Find the requested information.
AF  x  3 , BE  x  y , and CD  36 . Find x
and y .
5.
6. Find
x and y .
G
2x°
A
B
C
F
(5y+1)°
E
D
8. ABCD is a parallelogram, mBFC is 4 more than
twice the measure of EFC . Find the measure of ALL
angles.
x and y .
7. Find
43 °
C
B
D
98 °
z°
x°
56°
y°
A
9. Find all the lettered angles.
86° g°
39°
d°
F
E
10. The parallel sides of a trapezoid measure 8 units and
x 2 units, respectively. The midsegment of the trapezoid
measures 3x units. Find the value(s) of x .
f°
c°
e°
h°
b°
k°
m°
a°
18°
x which would result in
ABCD being an isosceles trapezoid. The figure is not
11. Determine the value(s) of
12. Kite ABCD . Find all missing angle and segment
measures.
drawn to scale.
A
12
B
3x
13
20
3x+8
5x-6
D
B
C
A
5
E
37°
23°
D
C
IV.
More Polygon Practice…
13. If the sum of the interior angles of a convex polygon is
14. If the measure of each exterior angle of a regular
1260 , what type of polygon is it?
convex polygon is
sum?
15. If the interior angles of a regular convex polygon each
16. If each interior angle of a regular convex polygon is five
times the measure of each exterior angle, what kind of
polygon is it?
measure 60 , what is the polygon’s exterior angle sum?
II.
24 , what is the polygon’s interior angle
Based on the definitions for each quadrilateral, use what you know to find the value of each variable.
17. quadrilateral ABCD
18. parallelogram MNOP
C
B
O
107°
x°
y°
y°
36°
z°
N
D
48°
x°
47°
P
M
A
19. rectangle QRST
R
20. rhombus ABCD with perimeter 88 units
S
2y°
122°
3z+1
(z+7)°
x°
y°
x°
T
Q
D
A
21. square JKLM
y+2
J
22. isosceles trapezoid EFGH with EH
Find the perimeter of the trapezoid, too.
K
x°
2y-5
M
C
B
L
2x+4
F
E
x
H
105°
3x+1
2x+1
y°
G
FG
III.
Properties of Kites and Trapezoids. Find the requested information.
23. Kite
EFGH . Find x and y .
24. Isosceles Trapezoid JKLM with JK
y , and z .
F
x°
18°
y°
E
20
J
G
I
K
x°
29°
36
z2-5z
128°
H
4y°
M
25. Kite ABCD with perimeter 86 feet.
and BD  4 x  6 . Find x and y .
BE  5x  15
26. Trapezoid JKLM with KL JM . Find
C
115°
(10y)°
(3x+5)°
M
J
3y
x and y .
L
(18y)°
6y-2
E
L
5z
K
B
A
ML . Find x ,
D
27. Kite KNML . Find
w , x , y , z , and the perimeter.
28. . Isosceles Trapezoid
Find x and y .
ABCD with midsegment EF .
N
w
z
4
L
3x+2
A
45°
K
B
64°
x
y
30°
2x+4
E
M
F
(5y+1)°
D
2x+1
C