Geometry
Chapter 6 Review
Name___________________________
Multiple Choice:
____
1. If
and
must be a parallelogram. The diagram is not to scale.
O
N
L
a.
M
c.
13
5
b.
5
x = 14, y =
13
____
5
13
d.
13
x = 14, y =
5
x = 8, y =
2. For the parallelogram, if
3
and
find
The diagram is not to scale.
1
a. 11
b. 156
3. If
scale.
find
A
c. 24
d. 166
so that quadrilateral ABCD is a parallelogram. The diagram is not to
B
D
C
a. 98
b. 262
d. 131
Find the value of each variable. The
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4. In the rhombus,
diagram is not to scale.
c. 49
3
2
1
|
|
____
x = 8, y =
4
2
____
find the values of x and y for which LMNO
a. x = 60, y = 150, z = 9
b. x = 30, y = 60, z = 9
c. x = 60, y = 60, z = 18
d. x = 30, y = 150, z = 18
____
5. Jill wants to build a square sandbox, but has no way of measuring angles. Explain how she can make
sure that the sandbox is square by only measuring length.
a. Arrange four equal-length sides so the diagonals bisect each other.
b. Not possible; Lucinda has to be able to measure a right angle.
c. Arrange four equal-length sides so the diagonals are equal lengths also.
d. Make each diagonal the same length as four equal-length sides.
____
6. Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain.
a.
b.
c.
d.
____
Yes; opposite angles are congruent.
Yes; both pairs of opposite sides are congruent.
Yes; two opposite sides are both parallel and congruent.
No; you cannot prove that the quadrilateral is a parallelogram.
7. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to
scale.
A
B
2x – 4
y + 25
a x b
. = .
6
,
y
=
7
____
6y – 5
x+ 3
D
C
8. Judging by appearances, which figure is a trapezoid?
a.
c.
b.
___
x c x d x
= . = . =
7,
7,
7
y
y
,
=
=
y
3
1
=
1
0
6
d.
9. Find the values of the variables in the parallelogram. The diagram is not to scale.
38
a.
b.
c.
d.
95
y°
z°
x°
____ 10. LMNO is a parallelogram. If NM = x + 11 and OL = 4x + 5, find the value of x and then find NM and OL.
O
a. x = 4, NM = 13, OL = 15
b. x = 4, NM = 15, OL = 15
____ 11. ABCD is a parallelogram. If
N
c. x = 2, NM = 15, OL = 13
d. x = 2, NM = 13, OL = 13
then
L
M
The diagram is not to scale.
A
a. 82
b. 98
c. 108
B
d. 164
D
C
____ 12. DEFG is a rectangle. DF = 4x – 4 and EG = x + 20. Find the value of x and the length of each diagonal.
a. x = 8, DF = 28, EG = 28
b. x = 4, DF = 24, EG = 24
c. x = 8, DF = 24, EG = 24
d. x = 8, DF = 28, EG = 30
•
____ 13. Judging by appearance, classify the figure in as many ways as possible.
____ 14. Which description does NOT guarantee that a quadrilateral is a rectangle?
a. a quadrilateral with all four angles right
b. a quadrilateral with all congruent angles
c. a quadrilateral with diagonals that are congruent and bisect each other
d. a parallelogram with congruent sides
•
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•
|
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rectangle, square, parallelogram
rhombus, trapezoid, quadrilateral, square
rectangle, square, quadrilateral, parallelogram, rhombus
square, rectangle, quadrilateral
•
a.
b.
c.
d.
____ 15. Find AM in the parallelogram if PN =14 and AO = 6. The diagram is not to scale.
M
N
A
P
O
a. 14
b. 12
c. 7
____ 16. WXYZ is a parallelogram. Name an angle congruent to
a.
b.
c.
X
Y
N
W
Z
d. 6
d.
____ 17. Which statement is true?
a. All quadrilaterals are rectangles.
b. All quadrilaterals are parallelograms.
c. All rectangles are quadrilaterals.
d. All quadrilaterals are squares.
Short Answer
18. For A(1, 2), B(3, 4), and C(6, 2), find all locations of a fourth point, D, so that a parallelogram is formed
using A, B, C, D in any order as vertices. Plot each point D on a coordinate grid and draw the
parallelogram.
6
6
6
5
5
5
4
4
4
3
3
3
2
2
2
1
1
-6 -5 -4 -3 -2 -1
-1
1 2 3 4 5 6
-6 -5 -4 -3 -2 -1
-1
1
1 2 3 4 5 6
-6 -5 -4 -3 -2 -1
-1
-2
-2
-2
-3
-3
-3
-4
-4
-4
-5
-5
-5
-6
-6
-6
1 2 3 4 5 6
19. Give the name that best describes the parallelogram and find the measures of the numbered angles.
The diagram is not to scale.
|
4
|
|
3
1
2
.
 
|
Geometry
Chapter 6
Vocabulary
Define:
1.) quadrilateral–
2.) trapezoid –
3.) parallelogram –
4.)rhombus –
5.) rectangle–
6.) square –
7.) diagonal –
8.) consecutive angles (adjacent angles)-
9.) kite
Chapter 6 review
Answer Section
MULTIPLE CHOICE
1. D
2. C
3. B
4. D
5. C
6. B
7. B
8. C
9. A
10. D
11. C
12. A
13. A
14. C
15. D
16. C
17. B
18 . A
19. C
20. D
21. D
22. C
23. A
24. C
SHORT ANSWER
25. 14
y
26.
y
8
B
4
D
–4
D
C
4
–8
B
8
x
–8
–4
A
C
4
8
x
–8
–4
D(4, 0)
–8
27. 10 cm , 26 cm
28. Rhombus; the measure of all numbered angles equal 27.5.
C
4
D
–4
–4
D(–2, 4)
B
4
A
–4
D(8, 4)
8
4
A
–8
y
8
–8
8
x