Download Do not write on this paper: Review work (Wednesday May 22 2013

Do not write on this paper:
Review work (Wednesday May 22 2013)
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
1. Judging by appearance, classify the figure in as many ways as possible.
____
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.
•
•
|
|
•
|
|
•
____
____
____
____
||
||
2x + 2
x+ 2
|
y–2
|
x + 11
a. x = 9, y = 13; 7, 15
c. x = 9, y = 13; 11, 20
b. x =13, y = 9; 7, 15
d. x =13, y = 9; 11, 11
3. What is the most precise name for quadrilateral ABCD with vertices A(–5, 2), B(–3, 6), C(6, 6), and
D(4, 2)?
a. quadrilateral
b. rectangle
c. parallelogram
d. rhombus
4. Which statement is true?
a. All quadrilaterals are rectangles.
b. All quadrilaterals are squares.
c. All rectangles are quadrilaterals.
d. All quadrilaterals are parallelograms.
5. Which Venn diagram is NOT correct?
a.
c.
Rhombuses
Quadrilaterals
Squares
Kites
b.
____
d.
Squares
Parallelograms
Rectangles
Rhombuses
6. Judging by appearances, which figure is a trapezoid?
a.
c.
b.
____
d.
7. ABCD is a parallelogram. If
A
D
then
B
C
The diagram is not to scale.
____
a. 66
b. 124
8. ABCD is a parallelogram. If
A
d. 132
The diagram is not to scale.
B
D
____
c. 114
then
C
a. 125
b. 65
c. 75
d. 115
9. LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5 find the value of x and then find NM and OL.
O
N
L
M
a. x = 7, NM = 20, OL = 22
b. x = 5, NM = 20, OL = 20
____ 10. For the parallelogram, if
3
2
and
c. x = 7, NM = 22, OL = 22
d. x = 5, NM = 22, OL = 20
find
The diagram is not to scale.
4
1
a. 9
b. 17
c. 173
d. 163
____ 11. Find the values of the variables in the parallelogram. The diagram is not to scale.
29
102
y°
z°
x°
a.
c.
b.
d.
____ 12. WXYZ is a parallelogram. Name an angle congruent to
X
Y
N
W
Z
a.
____ 13. In the parallelogram,
b.
c.
and
J
Find
d.
The diagram is not to scale.
K
O
M
L
a. 119
b. 61
c. 129
d. 68
____ 14. In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 4x – 5, and HE = 2y + 3. Find the values of x and y.
The diagram is not to scale.
D
E
H
G
F
a. x = 6, y = 3
b. x = 2, y = 3
c. x = 3, y = 2
____ 15. In the figure, the horizontal lines are parallel and
M
A
3
L
K
J
B
C
D
d. x = 3, y = 6
Find JM. The diagram is not to scale.
a. 9
b. 12
c. 6
____ 16. In the figure, the horizontal lines are parallel and
scale.
M
d. 3
Find KL and FG. The diagram is not to
A H
7.6
L
B
K
C
J
G
H
5.1
D
E
a. KL = 7.6, FG = 7.6
c. KL = 5.1, FG = 5.1
b.
d. KL = 7.6, FG = 5.1
____ 17. Find AM in the parallelogram if PN =9 and AO = 4. The diagram is not to scale.
M
N
A
P
O
a. 8
b. 4
c. 9
____ 18. What is the missing reason in the proof?
Given: parallelogram ABCD with diagonal
Prove:
A
D
Statements
1.
2.
3.
4.
5.
6.
d. 4.5
B
C
Reasons
1. Definition of parallelogram
2. Alternate Interior Angles Theorem
3. Definition of parallelogram
4. Alternate Interior Angles Theorem
5. Reflexive Property of Congruence
6. ?
a. Reflexive Property of Congruence
c. Alternate Interior Angles Theorem
b. ASA
d. SSS
____ 19. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to
scale.
A
B
4x – 2
y + 14
4y – 7
x + 28
D
C
a. x = 10, y = 38
b. x = 10, y = 21
c. x = 10, y = 7
d. x = 7, y = 10
____ 20. Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain.
a. Yes; opposite sides are congruent.
b. Yes; opposite angles are congruent.
c. No; you cannot prove that the quadrilateral is a parallelogram.
d. Yes; two opposite sides are both parallel and congruent.
____ 21. Based on the information given, can you determine that the quadrilateral must be a parallelogram?
Explain.
Given:
and
X
Y
N
W
Z
a. No; you cannot determine that the quadrilateral is a parallelogram.
b. Yes; two opposite sides are both parallel and congruent.
c. Yes; opposite sides are congruent.
d. Yes; diagonals of a parallelogram bisect each other.
____ 22. If
and
must be a parallelogram. The diagram is not to scale.
O
N
L
a.
b.
find the values of x and y for which LMNO
M
x = 9, y =
x = 0, y =
2
c.
5
2
d.
5
____ 23. If
scale.
find
A
x = 0, y =
x = 9, y =
5
2
5
2
so that quadrilateral ABCD is a parallelogram. The diagram is not to
B
D
C
a. 41
b. 139
c. 82
d. 278
____ 24. Which statement can you use to conclude that quadrilateral XYZW is a parallelogram?
X
Y
N
W
a.
b.
____ 25. In the rhombus,
diagram is not to scale.
Z
c.
d.
Find the value of each variable. The
|
|
3
1
|
|
2
____ 26.
____ 27.
____ 28.
____ 29.
a. x = 12, y = 84, z = 20
c. x = 6, y = 84, z = 10
b. x = 6, y = 174, z = 20
d. x = 12, y = 174, z = 10
DEFG is a rectangle. DF = 5x – 5 and EG = x + 11. Find the value of x and the length of each diagonal.
a. x = 4, DF = 13, EG = 13
c. x = 4, DF = 15, EG = 15
b. x = 4, DF = 15, EG = 18
d. x = 2, DF = 13, EG = 13
Lucinda 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. 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.
Which description does NOT guarantee that a quadrilateral is a parallelogram?
a. a quadrilateral with both pairs of opposite sides congruent
b. a quadrilateral with the diagonals bisecting each other
c. a quadrilateral with consecutive angles supplementary
d. quadrilateral with two opposite sides parallel
Find the values of a and b.The diagram is not to scale.
a°
36°
113°
b°
a.
c.
b.
d.
____ 30. The isosceles trapezoid is part of an isosceles triangle with a 46° 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.
a. 67°; 134°
b. 67°; 113°
c. 46°; 134°
d. 46°; 113°
____ 31. Find
in the kite. The diagram is not to scale.
1
|
D
39°
2
B
||
||
3
|
A
C
a. 51, 51
b. 39, 39
c. 39, 51
____ 32. Which description does NOT guarantee that a trapezoid is isoscles?
a. congruent diagonals
b. both pairs of base angles congruent
c. congruent bases
d. congruent legs
____ 33.
are base angles of isosceles trapezoid JKLM. If
a. 151
____ 34.
b. 1
Find
and
c. 29
The diagram is not to scale.
d. 51, 39
and
d. 75.5
R
|
|
S
||
||
U
T
a. 65
b. 70
c. 35
d. 80
____ 35. One side of a kite is 8 cm less than four times the length of another side. The perimeter of the kite is 78
cm. Find the lengths of the sides of the kite.
a. 9.4 cm and 29.6 cm
c. 23.5 cm
b. 23.5 cm and 86 cm
d. 9.4 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
Short Answer
37. Find the values of the variables and the lengths of the sides of this rectangle. The diagram is not to scale.
5x
2x + 6
5y
7y + 7
38. What type of quadrilateral has exactly one pair of parallel sides?
39. Isosceles trapezoid ABCD has legs
10, find the value of y.
and
and base
If AB = 4y – 3, BC = 3y – 4, and CD = 5y –
40. Judging by appearance, classify the figure in as many ways as possible using rectangle, trapezoid, square,
quadrilateral, parallelogram, rhombus.
41. For A(1, –1), B(–1, 3), and C(4, –1), 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.