Name ________________________________________ Period _____ Date __________
GEOMETRY
UNIT #8 Review
Define the following vocabulary terms:
1.
2.
3.
4.
5.
6.
7.
kite
trapezoid
rectangle
polygon
square
rhombus
parallelogram
8. Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides.
a.
b.
c.
d.
polygon, decagon
polygon, hexagon
polygon, dodecagon
not a polygon
9. Tell whether the polygon is regular or irregular. Circle one.
regular or irregular
convex or concave
10. The door on a spacecraft is formed with 6 straight panels that overlap to form a regular hexagon.
What is the measure of YXZ ?
X
Z
Y
m YXZ  60
m YXZ  120
a.
b.
c.
d.
m YXZ  720
m YXZ  45
11. The diagram shows the parallelogram-shaped component that attaches a car’s rearview mirror to the
car. In RSTU , UR  25 , RX  16 , and m STU  42.4 . Find ST , XT , and m RST .
S
T
X
R
U
12. MNOP is a parallelogram. Find MP.
M
N
5x
3x+12
P
a.
b.
O
MP  25
MP  30
c.
d.
MP  20
MP  6
13. Three vertices of WXYZ are X (2, 3) , Y (0, 5) , and Z (7, 7) . Find the coordinates of vertex W.
a.
b.
c.
d.
(4, 0)
(9, 15)
(5, 0)
(5, –1)
14. Show that GHIJ is a parallelogram for x  5 and y  8 .
H
5x-10
I
3y
G
5y-16
7x-20
J
15. KL  MN and
your answer.
KLM  MNK . Determine if the quadrilateral must be a parallelogram. Justify
M
L
K
N
a. No. Only one set of angles and sides are given as congruent. The conditions for a parallelogram are not
met.
b. Yes. Opposite angles are congruent to each other. This is sufficient evidence to prove that the
quadrilateral is a parallelogram.
c. Yes. Opposite sides are congruent to each other. This is sufficient evidence to prove that the
quadrilateral is a parallelogram.
d. Yes. One set of opposite sides are congruent, and one set of opposite angles are congruent. This is
sufficient evidence to prove that the quadrilateral is a parallelogram.
16. Using the picture and the given information to the right, explain, in words, why DEFG must be a
parallelogram.
y
slope of DE 
10  7
3

3  (5) 8
slope of FG 
4 1 3

80 8
E (3,
. 10)
10
D(-5,7)
5
F(8, 4)
DE  (3  (5)) 2  (10  7) 2  73
G (0,1)
–5
5
x
FG  (8  0) 2  (4  1) 2  73
17. Show that all four sides of square ABCD are congruent and that AB  BC .
y
5
4
B
3
2
1
C
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
x
–2
–3
A
–4
–5
–6
–7
D
18. Determine if the conclusion is valid. If not, tell what additional information is needed to make it
valid.
Given: AB  CD, BC  DA and AC  BD
Conclusion: ABCD is a square.
A
B
D
C
a. Opposite sides are congruent, so ABCD is a parallelogram.
Diagonals are congruent, so ABCD is a rectangle.
Two consecutive sides are not congruent, so ABCD is not a square.
b. Opposite sides are congruent, so ABCD is a rhombus.
Diagonals are congruent, so ABCD is a rectangle.
A quadrilateral that is a rhombus and a rectangle is a square, so ABCD is a square.
c. Opposite sides are congruent, so ABCD is a parallelogram.
Diagonals are congruent, so ABCD is a rhombus.
One angle is not a right angle, so ABCD is not a square.
d. Opposite sides are congruent, so ABCD is a rhombus.
Diagonals are congruent, so ABCD is a square.
19. Use the diagonals to determine whether a parallelogram with vertices A(1, 2), B(2, 0),
C (0,1) and D (1, 1) is a rectangle, rhombus, or square. Mark all the names that apply.
I. rectangle
II. rhombus
III. square
20. In parallelogram LMNO, NO  13.5 and LO  15 . What is the perimeter of parallelogram LMNO?
21. Find the value of x in the rhombus.
2
(-4 x + 15)
2
(8 x + 24x )