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Geometry: Chapter 6 Study Guide
1. In the rhombus,
What are
The diagram is not to scale.
|
1
|
1
24º
3
3
|
|
2
2
2. In the parallelogram,
Find
to scale.
and
The diagram is not
5. In quadrilateral ABCD,
and
. For what value of x is ABCD a
rhombus?
A
J
B
K
O
D
M
L
6. The sum of the angle measures of a polygon with s
sides is 2340. Find s.
3. Find AM in the parallelogram if PN =15 and AO =
6. The diagram is not to scale.
M
C
7. Find the missing values of the variables. The
diagram is not to scale.
N
119°
x°
106° y°
A
P
O
74°
8.
What is LM?
A
4. Find the measure of the numbered angles in the
rhombus. The diagram is not to scale.
L
D
B
M
C
9. Find
to scale.
in the kite. The diagram is not
15. In the figure, the horizontal lines are parallel and
Find KL and FG. The diagram is
not to scale.
|
D
3
1
|
A
17°
14. What is the measure of one angle in a regular
30-gon?
2
M
B
A H
8.7
B
G
||
||
L
K
C
C
J
F
8.6
D
E
10. How many sides does a regular polygon have if
each exterior angle measures 30?
11. In the parallelogram,
Find
scale.
and
The diagram is not to
A
P
E
D
C
17. ABCD is a parallelogram. If
then
The diagram is not to scale.
R
A
12. LMNO is a parallelogram. If NM = x + 5 and OL =
2x + 3, find the value of x and then find NM and
OL.
O
B
Q
O
S
16. In quadrilateral ABCD,
and
. For what value of x is ABCD a
rectangle?
B
N
D
L
M
13. What is the most precise name for quadrilateral
ABCD with vertices A(–5, 2), B(–3, 5), C(4, 5), and
D(2, 2)?
C
18. Find the values of the variables and the lengths of
the sides of this kite.
y–3
|
x+ 2
||
||
|
2x + 2
x + 11
19. Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain why or
why not.
Given:
and
X
Y
N
W
Z
20. For the parallelogram, if
find
scale.
3
2
and
The diagram is not to
K
L
N
M
4
1
21. In rectangle KLMN, KM =
and LN = 64.
Find the value of x.
22. Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain why or why not.
23. Find the value of x. The diagram is not to scale.
A
B
(3x + 10)º
148º
(x)º
D
C
27.
112º
What is
the value of x?
A
B
24. Find the values of a and b. The diagram is not to
scale.
L
a°
M
109°
D
65°
b°
C
28. In the rhombus,
Find
the value of each variable. The diagram is not to
scale.
|
|
25. In rectangle PQRS, PR = 18x – 28 and QS = x +
380. Find the value of x and the length of each
diagonal.
P
Q
3
1
|
|
2
S
R
26. ABCD is a parallelogram. If
then
The diagram is not to scale.
29. What is the sum of the angle measures of a 35-gon?
30.
JKLM. If
are base angles of isosceles trapezoid
and
31. If
find
so that
quadrilateral ABCD is a parallelogram. The
diagram is not to scale.
A
36. This jewelry box has the shape of a regular
pentagon. It is packaged in a rectangular box as
shown here. The box uses two pairs of congruent
right triangles made of foam to fill its four corners.
Find the measure of the foam angle marked.
B
D
C
32. Parallelogram ABCD has the angle measures
shown. Can you conclude that it is a rhombus, a
rectangle, or a square? Explain.
x
37.
66º
66º
and
diagram is not to scale.
Find
The
R
|
66º
66º
x
|
U
S
34. DEFG is a rectangle. DF = 5x – 3 and EG = x + 5.
Find the value of x and the length of each diagonal.
35. Find values of x and y for which ABCD must be a
parallelogram. The diagram is not to
scale.
A
B
||
||
33. A road sign is in the shape of a regular pentagon.
What is the measure of each angle on the sign?
Round to the nearest tenth.
T
38. Find
. The diagram is not to scale.
96°
118°
115°
3x – 14
y + 11
104°
A
4y – 7
x+ 2
D
C
39. In the figure, the horizontal lines are parallel and
Find JM. The diagram is not to
scale.
M
A
9
L
K
J
B
C
D
40. Find the sum of the measures of the angles of the
figure.
41. Find the values of the variables in the
parallelogram. The diagram is not to scale.
31
96
y°
z°
x°
Geometry: Chapter 6 Study Guide
Answer Section
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41.
120
6
4
15
x = 93, y = 74
88
12 sides
64
x = 2, NM = 7, OL = 7
parallelogram
168
KL = 8.7, FG = 8.6
12
123
x = 9, y = 14; 11, 20
Yes; diagonals of a parallelogram bisect each other.
164
4
Yes; the diagonals bisect each other.
45
x = 24, PR = 404, QS = 404
63
35
x = 6, y = 84, z = 3
5940
154
134
Parallelogram ABCD is a rhombus, because the diagonal bisects two angles.
108
x = 2, DF = 7, EG = 7
x = 8, y = 6
72°
20
73
27
540