GEOM. CH. 6 REVIEW QUADRILATERALS
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Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Judging by appearance, classify the figure in as many ways as
possible.
____
d. parallelogram
•
____
a. quadrilateral b. rectangle c. rhombus
4. Which statement is true?
a. All parallelograms are rectangles.
b. All rectangles are squares.
c. All quadrilaterals are parallelograms.
d. All parallelograms are quadrilaterals.
5. Which Venn diagram is NOT correct?
a.
c.
Quadrilaterals
Squares
Kites
•
•
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•
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Rhombuses
y–4
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____
Squares
Parallelograms
Rectangles
Rhombuses
x+ 5
____
2x + 4
d
.
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____
b
.
a. rectangle, square, quadrilateral, parallelogram, rhombus
b. rectangle, square, parallelogram
c. rhombus, trapezoid, quadrilateral, square
d. square, rectangle, quadrilateral
2. Find the values of the variables and the lengths of the sides of this
kite.
x+ 6
a. x = 2, y = 11; 2, 16
c. x = 2, y = 11; 7, 8
b. x =11, y = 2; 2, 16
d. x =11, y = 2; 7, 7
3. What is the most precise name for quadrilateral ABCD with vertices
A(–5, 2), B(–3, 4), C(5, 4), and D(3, 2)?
6. Judging by appearances, which figure is a trapezoid?
a.
c.
b.
d.
a. x = 9, NM = 29, OL = 31
c. x = 7, NM = 29, OL = 29
b. x = 9, NM = 31, OL = 31
d. x = 7, NM = 31, OL = 29
____ 10. For the parallelogram, if
and
find
The diagram is not to scale.
3
____
7. ABCD is a parallelogram. If
The diagram is not to scale.
A
then
4
2
B
1
a. 140
b. 16
c. 150
d. 40
____ 11. Find the values of the variables in the parallelogram. The diagram is
not to scale.
33
D
____
117
C
a. 103
b. 154
8. ABCD is a parallelogram. If
The diagram is not to scale.
c. 113
d. 77
then
y°
A
B
z°
x°
a.
c.
b.
d.
____ 12. WXYZ is a parallelogram. Name an angle congruent to
D
____
C
X
Y
a. 76
b. 129
c. 119
d. 61
9. LMNO is a parallelogram. If NM = x + 22 and OL = 3x + 8 find the
value of x and then find NM and OL.
O
N
N
W
L
M
a.
Z
b.
c.
d.
____ 13. In the parallelogram,
The diagram is not to scale.
and
J
Find
____ 16. In the figure, the horizontal lines are parallel and
Find KL and FG. The diagram is not to scale.
K
M
A H
7.7
L
B
G
O
K
C
J
M
H
7.5
D
L
E
a. 58
b. 50
c. 108
d. 98
a. KL = 7.7, FG = 7.7
c. KL = 7.5, FG = 7.5
____ 14. In parallelogram DEFG, DH = x + 4, HF = 3y, GH = 3x – 1, and HE
b. KL = 7.7, FG = 7.5
d.
= 5y + 3. Find the values of x and y. The diagram is not to scale.
____ 17. Find AM in the parallelogram if PN =10 and AO = 4. The diagram is
not to scale.
D
E
M
N
A
H
G
F
P
O
a. x = 11, y = 5 b. x = 5, y = 11 c. x = 8, y = 4 d. x = 4, y = 8
____ 15. In the figure, the horizontal lines are parallel and
a. 4
b. 5
c. 8
Find JM. The diagram is not to scale.
____ 18. What is the missing reason in the proof?
Given: parallelogram ABCD with diagonal
M
A
Prove:
4
L
K
J
a. 12
B
A
B
C
D
b. 4
c. 16
d. 8
D
C
d. 10
Statements
Reasons
1. Definition of parallelogram
1.
2.
2. Alternate Interior Angles
Theorem
3. Definition of parallelogram
3.
4.
4. Alternate Interior Angles
Theorem
5. Reflexive Property of
Congruence
6. ?
5.
6.
a. ASA
c. Reflexive Property of
Congruence
b. SSS
d. Alternate Interior Angles
Theorem
____ 19. Find values of x and y for which ABCD must be a parallelogram.
The diagram is not to
scale.
A
a. Yes; two opposite sides are both parallel and congruent.
b. Yes; opposite angles are congruent.
c. Yes; opposite sides are congruent.
d. No; you cannot prove that the quadrilateral is a parallelogram.
____ 21. Based on the information given, can you determine that the
quadrilateral must be a parallelogram? Explain.
Given:
and
X
B
Y
N
2x – 0
y + 10
W
Z
a. Yes; opposite sides are congruent.
b. Yes; diagonals of a parallelogram bisect each other.
x+ 2
c. No; you cannot determine that the quadrilateral is a
parallelogram.
d.
Yes; two opposite sides are both parallel and congruent.
D
C
____ 22. If
and
find the
values of x and y for which LMNO must be a parallelogram. The
a. x = 2, y = 4 b. x = 2, y = 16 c. x = 6, y = 2 d. x = 2, y = 6
diagram is not to scale.
____ 20. Based on the information in the diagram, can you prove that the
figure is a parallelogram? Explain.
O
N
4y – 8
L
M
a.
b. x = 90, y = 45, z = 6
d. x = 90, y = 135, z = 3
____ 26. DEFG is a rectangle. DF = 2x – 1 and EG = x + 3. Find the value of
b.
d.
4
3
x and the length of each diagonal.
x = 10, y =
x = 1, y =
a. x = 2, DF = 5, EG = 5
c. x = 4, DF = 5, EG = 5
3
4
b.
x
=
4,
DF
=
7,
EG
=
9
d. x = 4, DF = 7, EG = 7
____ 23. If
find
so that quadrilateral ABCD is a
____ 27. Lucinda wants to build a square sandbox, but has no way of
parallelogram. The diagram is not to scale.
measuring angles. Explain how she can make sure that the sandbox
A
B
is square by only measuring length.
a. Arrange four equal-length sides so the diagonals bisect each
other.
b. Arrange four equal-length sides so the diagonals are equal
lengths also.
c. Make each diagonal the same length as four equal-length sides.
d. Not possible; Lucinda has to be able to measure a right angle.
D
C
____ 28. Which description does NOT guarantee that a quadrilateral is a
a. 140
b. 80
c. 40
d. 280
rectangle?
____ 24. Which statement can you use to conclude that quadrilateral XYZW is
a. a quadrilateral with all four angles right
a parallelogram?
b. a quadrilateral with all congruent angles
c. a parallelogram with congruent sides
X
Y
d. a quadrilateral with diagonals that are congruent and bisect each
other
____ 29. Find the values of a and b.The diagram is not to scale.
x = 1, y =
c.
4
3
x = 10, y =
3
4
N
a°
W
103°
Z
a.
b.
c.
d.
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____ 25. In the rhombus,
the value of each variable. The diagram is not to scale.
3
1
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|
2
a. x = 45, y = 45, z = 3
c. x = 45, y = 135, z = 6
61°
b°
Find
a.
c.
b.
d.
____ 30. The isosceles trapezoid is part of an isosceles triangle with a 48°
vertex angle. What is the measure of an acute base angle of the
trapezoid? Of an obtuse base angle? The diagram is not to scale.
R
|
|
S
a. 48°; 114°
____ 31. Find
b. 48°; 132°
c. 66°; 132°
d. 66°; 114°
in the kite. The diagram is not to scale.
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3
1
2
B
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D
21°
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A
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U
T
a. 10
b. 110
c. 20
d. 60
____ 35. One side of a kite is 7 cm less than four times the length of another
side. The perimeter of the kite is 65 cm. Find the lengths of the
sides of the kite.
a. 19.75 cm
c. 7.9 cm and 24.6 cm
b. 19.75 cm and 72 cm
d. 7.9 cm
____ 36. In quadrilateral MNOP,
Which of a parallelogram,
trapezoid, or rhombus could quadrilateral MNOP be?
a. parallelogram or rhombus
c. trapezoid only
b. parallelogram only
d. any of the three
C
a. 21, 69
b. 69, 69
c. 21, 21
d. 69, 21
Short Answer
____ 32. Which description does NOT guarantee that a quadrilateral is a
kite?
37. Find the values of the variables and the lengths of the sides of this
a. one diagonal bisects opposite angles and the other diagonal does
rectangle. The diagram is not to scale.
not
7x
b. two distinct pairs of congruent adjacent sides
c. perpendicular diagonals
d. perpendicular diagonals, exactly one of which bisects the other
____ 33.
are base angles of isosceles trapezoid JKLM. If
4x + 8
3y
and
a. 1
b. 151
c. 29
d. 75.5
____ 34.
and
Find
The diagram is not to scale.
3y + 13
38. What type of quadrilateral has two pairs of parallel sides?
39. Isosceles trapezoid ABCD has legs
and
and base
If
AB = 6y – 7, BC = 2y – 7, and CD = 7y – 13, find the value of y.
40. One side of a kite is 5 cm less than 3 times the length of another.
The perimeter of the kite is 62 cm. Find the length of each side of
the kite.
4
3
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41. For parallelogram PQRS, find the values of x and y. Then find PT,
TR, ST, and TQ. The diagram is not to scale.
|
1
2
 
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44. Draw two noncongruent kites A and B such that the sides of kite A
are congruent to the sides of kite B.
45. Judging by appearance, classify the figure in as many ways as
possible using rectangle, trapezoid, square, quadrilateral,
parallelogram, rhombus.
42. Complete this statement: For parallelogram ABCD,
Then state a definition or theorem that justifies your answer.
D
C
O
A
B
43. Give the name that best describes the parallelogram and find the
measures of the numbered angles. The diagram is not to scale.
A
C
D
D
B
C
A
D
C
A
A
A
C
C
A
B
A
A
D
B
B
B
A
A
A
D
B
C
C
D
A
C
B
C
C
43. ANS:
Rhombus; the measure of all numbered angles equal 31.
44. ANS:
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37. ANS:
x = 7, y = 12; 36, 49
38. ANS:
parallelogram
39. ANS:
6
40. ANS:
9 cm , 22 cm
41. ANS:
x = 3, y = 6; 5, 5, 7, 7
42. ANS:
OD; the diagonals of a parallelogram bisect each other.
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MULTIPLE CHOICE
36. ANS: D
SHORT ANSWER
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GEOM. CH. 6 REVIEW "QUADRILATERALS"
Answer Section
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45. ANS:
trapezoid, quadrilateral