Quads
Date:
Name:
1.
2.
3.
In the accompanying diagram of rhombus ABCD,
the lengths of the sides AB and BC are represented
by 3x 4 and 2x + 1, respectively. Find the value
of x.
4.
In the accompanying gure, ABCD is a
parallelogram, mOA = 2x + 35, and mOC = 5x 22.
Find the value of x.
5.
In the accompanying diagram of rhombus ABCD,
the lengths of sides AB and BC are represented
by 3x 8 and 2x + 1, respectively. Find the value
of x.
6.
The perimeter of a square is 20x 4. Which
expression represents a side of the square in terms
of x ?
In the accompanying diagram of parallelogram
ABCD, mOA = 2x 10 and mOB = 5x + 15.
Find x.
In the parallelogram ABCD, mOA = 2x + 50 and
mOC = 3x + 40. The measure of O A is
A.
18
B.
20
C.
70
D. 86
page 1
A.
5x
C.
8x
B.
16
10x
D. 5x
2
1
7.
In the accompanying diagram of rectangle ABCD,
diagonal AC = 8x + 4 and diagonal BD = 5x + 16.
Find the value of x.
11.
In the accompanying diagram of parallelogram
ABCD, diagonals AC and intersect BD at E,
BE = 2x and ED = x 10.
What is the value of x?
A.
8.
30
B.
30
C.
6
D. 6
In the accompanying diagram, ABCD is a
parallelogram with mOB = 120, mOC = 60,
mOD = 2x + 5y, and mOA = 4x + y. Find the
values of x and y. Check your solution.
12.
9.
The diagonals of rectangle ABCD intersect at E. If
DE = 3x + 1 and AC = 5x + 4, nd the value of x.
10.
If the measures of two opposite angles of an
isosceles trapezoid are 2x + 20 and 3x, what is the
value of x ?
page 2
In the diagram below of isosceles trapezoid DEFG,
DE k GF, DE = 4x 2, EF = 3x + 2, FG = 5x 3,
and GD = 2x + 5. Find the value of x.
Quads
13.
In the diagram below of quadrilateral ABCD
with diagonal BD, mOA = 93, mOADB = 43,
mOC = 3x + 5, mOBDC = x + 19, and
mODBC = 2x + 6. Determine if AB is parallel to
DC. Explain your reasoning.
16.
In rectangle MATH, AT = 8 and TH = 12. Find
the length of diagonal HA to the nearest tenth.
17.
The perimeter of a rhombus is 60. If the length
of its longer diagonal measures 24, the length of
the shorter diagonal is
A.
14.
B.
15
C.
18
D. 20
What is the length of a diagonal of a rectangle
whose sides are 3 and 7?
18.
15.
9
The diagonals of a rhombus are 10 centimeters and
24 centimeters. A side of the rhombus measures
A.
10 cm
B.
13 cm
C.
24 cm
In the diagram below, LATE is an isosceles
trapezoid with LE = AT, LA = 24, ET = 40, and
AT = 10. Altitudes LF and AG are drawn.
What is the length of LF?
D. 26 cm
A.
page 3
6
B.
8
C.
3
D. 4
Quads
19.
21.
In rhombus ABCD, with diagonals AC and DB,
AD = 10.
In the accompanying diagram of rhombus RUDE,
mORUE = 21 and UE = 20.
Find, to the nearest tenth, the
a) length of RD
b) perimeter of RUDE
If the length of diagonal AC is 12, what is the
length of DB?
A.
8
B.
16
C.
p
44
D.
p
136
22.
In the accompanying diagram, STAR is an isosceles
trapezoid with SR = TA, ST = 20, RA = 30,
mOSRA = 40, and altitudes SE and TF are drawn
a) Find SE to the nearest tenth.
b) Find SR to the nearest tenth.
20.
In the accompanying diagram of rhombus ABCD,
mOBAD = 36 and the length of diagonal AEC = 16.
c) Find the perimeter of trapezoid STAR to the
nearest integer.
d) Find the area of trapezoid STAR to the
nearest integer.
a) Find the length of diagonal BD to the nearest
tenth.
b) Find the perimeter of rhombus ABCD to the
nearest integer.
page 4
Quads
23.
In the diagram below, quadrilateral STAR is a
rhombus with diagonals SA and TR intersecting
at E. ST = 3x + 30, SR = 8x 5, SE = 3z,
TE = 5z + 5, AE = 4z 8, mORTA = 5y 2, and
mOTAS = 9y + 8. Find SR, RT, and mOTAS .
25.
In isosceles trapezoid ABCD, mO D = 70, AB = 6,
and DC = 14.
a) Find DE.
b) Find the altitude AE to the nearest integer.
c) Using the answer to part b, nd the area of
trapezoid ABCD.
d) Find AD to the nearest integer.
24.
In the accompanying diagram, square ADFE is
inscribed in rectangle ABCD, EB : AB = 3 : 7, and
the perimeter of ABCD is 132.
26.
Find:
In the accompanying diagram, diagonals TA and
EM of rhombus TEAM intersect at point S. The
length of diagonal TA is 30 and anglemSAM = 53.
a) Find the length of side MA to the nearest
integer.
a) the length of AE
b) the area of rectangle ABCD
b) Find the length of diagonal EM to the
nearest integer.
c) the ratio of the area of rectangle EBCF to
the area of rectangle ABCD, in simplest form
c) Find the perimeter of ^EMA to the nearest
integer.
page 5
Quads
27.
In the accompanying diagram of rhombus ABCD,
diagonal AC = 80 and mOBAC = 36.
30.
a) Find the length of a side of the rhombus to
the nearest tenth.
b) Using your answer in part a,
perimeter of rhombus ABCD.
nd the
c) Find the length of diagonal to the nearest
integer.
28.
In the accompanying diagram of rhombus QRST,
diagonals QS and RT intersect at M. Which
statement must be true?
A.
Triangle QRM is an isosceles right triangle.
B.
^QRM = ^SRM
C.
Triangle QRM is an obtuse triangle.
D. QS = RT
Which property is not true for all parallelograms?
A.
Opposite angles are congruent.
B.
Consecutive angles are supplementary.
C.
Opposite sides are congruent.
31.
If quadrilateral ABCD is a parallelogram, which
statement must be true?
D. Diagonals are congruent.
29.
A quadrilateral has diagonals that are congruent
but not perpendicular. The quadrilateral contains
no right angles. The quadrilateral could be
A.
a square
B.
an isosceles trapezoid
C.
a rectangle
A.
AC ? BD
B.
AC = BD
C.
AC bisects ODAB and O BCD.
D. AC and BD bisect each other.
D. a rhombus
page 6
Quads
32.
In the diagram below, parallelogram ABCD has
diagonals AC and BD that intersect at point E.
33.
The length of a rectangle is 3 inches more than
its width. The area of the rectangle is 40 square
inches. What is the length, in inches, of the
rectangle?
A.
5
B.
8
C.
8.5
D. 11.5
Which expression is not always true?
A.
ODAE = OBCE
B.
C.
AC = DB
D. DE = EB
ODEC = OBEA
34.
In rhombus ABCD, the diagonals AC and BD
intersect at E. If AE = 5 and BE = 12, what is the
length of AB?
A.
35.
B.
10
C.
13
D. 17
The diagonals of a rhombus have lengths of 16
and 30. The length of a side of the rhombus is
A.
page 7
7
17
B.
p
15 2
C.
p
16 2
D. 34
Quads
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Quads
02/10/2016
1.
Answer:
5
21.
Answer:
7.7; 42.8
2.
Answer:
25
22.
Answer:
4.2; 6.5; 63; 105
3.
Answer:
C
23.
Answer:
SR = 51, RT = 90, mOTAS = 62
4.
Answer:
19
5.
Answer:
24.
Answer:
24; 1,008; 3 : 7
9
6.
Answer:
25.
Answer:
4; 11; 110; 12
D
7.
Answer:
26.
Answer:
25; 40; 90
4
8.
Answer:
27.
Answer:
49.4; 197.6; 58
(10; 20)
9.
Answer:
28.
Answer:
D
2
10.
Answer:
29.
Answer:
B
32
11.
Answer:
30.
Answer:
B
B
12.
Answer:
31.
Answer:
D
3
13.
Answer:
32.
Answer:
C
Parallel
14.
Answer:
33.
Answer:
B
p
58
15.
Answer:
34.
Answer:
C
B
16.
Answer:
35.
Answer:
A
14.4
17.
Answer:
C
18.
Answer:
A
19.
Answer:
B
20.
Answer:
5.2; 34