1
ACT
Section (1)
1 . In the figure below, measure of BAC is 35,
the measure of ABC is 115, what is the
measure ACD?
A
Geometry
4. In ABC shown below, ̅̅̅̅ ̅̅̅̅ and the measure
of A is 48. What is the measure of C?
C
35
48
A
115
C
B
B
A. 48
B. 84
C. 90
D. 96
E. 132
D
A. 115
B. 120
C. 125
D. 145
E. 150
2. In the figure below, the measure of XAB is 150,
the measure of YCB is 81, and X, A, C, and Y
are collinear. What is the measure of B ?
5. In the figure below, QPR is 40, PQR is 105,
And points Q, R, and S are collinear.
What is the measure of PRS ?
P
F. 105
G. 125
H. 130
J. 140
K. 145
F. 30
G. 51
H. 60•
J. 69•
K. 77•
105
?
S
R
Q
6. In the figure below, ̅̅̅̅ is congruent to ̅̅̅̅ , and
̅̅̅̅ and ̅̅̅̅ intersect ̅̅̅̅ at C. what is the measure
of B?
B
3. In the figure below, what is the value of x?
?
x
x
C
E
38
A
107
A. 35
B. 38
C. 72
D. 107
E. 145
Mr . Mosaad El Geneady
35
A. 14
B. 38
C. 76
D. 104
E. 142
Mo: 01001851053
F
2
ACT
7. In the figure below, C is on ̅̅̅̅ , BAC is 42,
and ABC is 108, What is the measure of
ACD ?
A
Geometry
10. In the figure below, BAC measures 35,
ABC is 95, and points B, C, and D are collinear
What is the measure of ACD ?
A
42
?
108
B
C
D
A. 108
B. 120
C. 132
D. 138
E. 150
35
F. 95
G. 125
H. 130
J. 140
K. 145
95
B
?
C
D
11. The figure is shows lines ⃡ and ⃡ , line
segments ̅̅̅̅ and ̅̅̅̅ , and 2 angle measures.
What is the measure of ACB ?
8. Three line segments intersect as shown in the
figure below, forming angles with measure of
150, 40, and x, respectively . What is the value
of x?
F. 38
G. 42
H. 48
J. 55
K. 77
F.
G.
H.
J.
K.
12. In the figure below, C lies on both ̅̅̅̅ and ̅̅̅̅ ,
̅̅̅̅ and ̅̅̅̅ are parallel and congruent, and 2 angle
measures are given. What is the measure ofACB ?
95
85
80
75
70
9. In the figure below, ⃡ intersects ⃡ at C and is
perpendicular to ⃡ . Line ⃡ intersects ⃡ at F.
Given that the measure of EFG is 25, what is
the measure of BCD?
F. 65
G. 115
H. 120
J. 130
K. 155
Mr . Mosaad El Geneady
F. 55
G. 57.5
H. 65
J. 67.5
K. 70
13. In The above figure, l //m. What is the value of x?
A) 40
B) 25
C) 20
Mo: 01001851053
D) 15
E) 10
ACT
14. In the figure below, Vertices D and F of DEF
lie on ̅̅̅̅ , the measure of CDE is 148, and
the measure of EFG is 140. What is the
measure of DEF ?
F. 72
G. 98
H. 100
J. 108
K. 116
15. Given the triangle shown below with exterior
angles that measure x°, y°, and z° as shown,
what is the sum of x, y, and z ?
F. 180
G. 231
H. 309
J. 360
K. Cannot be determined from the given information
16. In the figure below, C is the intersection of ̅̅̅̅
and ̅̅̅̅ . If it can be determined, what is the
measure of ∠BAC ?
A. 080°
B. 100°
C. 110°
D. 115°
E. Cannot be determined from the given information
Mr . Mosaad El Geneady
3
Geometry
17. In the figure below, BAC measures 30°,
ABC measures 110°, and points B, C, and D
are collinear. What is the measure of ACD ?
F. 150°
G. 140°
H. 130°
J. 120°
K. 110°
18. In the figure below, A,D,C, and E are collinear.
̅̅̅̅, ̅̅̅̅, and ̅̅̅̅ are all the same length, and the
angle measure of ABD is 25. What is the
measure of BCE ?
F. 50
G. 100
H. 105
J. 130
K. 160
19. In the figure below, lines m and n are parallel,
transversals r and s intersect from an angle of
measure x, and 2 other angle measures are as
marked. What is the value of x?
A. 15
B. 25
C. 35
D. 65
E. 80
Mo: 01001851053
ACT
20. The figure below shows quadrilateral ABCD ,
What is the measure of C?
F. 120
G. 115
H. 105•
J. 100•
K. 80•
21. In the figure below, B is on ̅̅̅̅ , E is on ̅̅̅̅ , ̅̅̅̅ is
parallel to ̅̅̅̅ and ̅̅̅̅ is congruent to ̅̅̅̅ . What
is the measure of DEB ?
F. 35
G. 135
H. 145•
J. 155•
K. 215•
22. In the figure below, ̅̅̅̅ is perpendicular to ̅̅̅̅ ,
the measure of CED is 38, what is the measure
of AEB ?
F. 38
G. 45
H. 52•
J. 71•
K. 76•
Mr . Mosaad El Geneady
4
Geometry
23. In the figure below, measure of ABE is 75,
the measure of ABC is 25, and the measure
of DBE is 35. What is the measure ABD
A. 15
B. 30
C. 40
D. 50
E. 60
24. In the figure below, ABCD is a trapezoid, E lies
on ⃡ , and angle measures are as marked, What
is the measure of BDC?
F. 15
G. 25
H. 30
J. 35
K. 45
25. In the figure below, ̅̅̅̅̅ intersect ̅̅̅̅ at Y, the
measure of XYV is ( 3x + 5), and the measure
of ZYW is ( 4x – 6). What is the measure of
XYZ ?
F. 83
G . 97
H. 104
J. 142
K. 160
Mo: 01001851053
5
ACT
26. In ABC below, the measure of ABC is 70, the
measure ACB is 32, D is on ̅̅̅̅ , and ̅̅̅̅ is a
bisector of BAC. What is the measure of ADB
Geometry
29. The parallelogram below has consecutive angles
with measure xand 25. What is the value of x?
C
32
A. 100
B. 115
C. 130
D. 140
E. 155
D
A. 64
B. 70
C. 71
D. 78
E. 102
70
A
x
25
B
27. In the figure below, line m is perpendicular to
line n, and line p is parallel to line q, Lines m. n,
and p intersecting at a single point. Some angle
measures are given. What is the value of x?
30. In the figure below, 5 angles measure are given.
The angle marked with measure of yis an
exterior angle. What is the value of y?
( x + 25 )
( 2x + 10 )
( 3x – 25 )
F. 32
G. 58
H. 122
J. 148
K. 158
Mr . Mosaad El Geneady
y
F. 22.5
G. 45
H. 80
J. 100
K. 145
31. In the figure below ,B lie on ̅̅̅̅ , E lie on ̅̅̅̅ ,
̅̅̅̅ // ̅̅̅̅ , DBF is isosceles with ̅̅̅̅ ̅̅̅̅ ,
and CBF is 32. What is the measure of BED?
28. In the figure below, E is on ̅̅̅̅ , and the measure
of BED and AEB are 90 and 145,
respectively. If it can be determined, what is the
measure of CED?
A. 35
B. 45
C. 55
D. 80
E. Cannot be determined from the given information
( 2x – 10 )
F. 106
G. 116
H. 122
J. 132
K. 148
Mo: 01001851053
6
ACT
32. In the figure below, A is on ⃡ and C is on ⃡
What is the measure of ABC ?
.
A. 24
B. 42
C. 45
D. 48
E. 66
33. In ACD below, B is on ̅̅̅̅ , the measure of
CAD is 28, and ̅̅̅̅ is perpendicular to both ̅̅̅̅
And ̅̅̅̅. What is the measure of CBE?
Geometry
35. For trapezoid ABCD shown below, AB//DC, the
measures of the interior angles are distinct, and the
measure of D is x. What is the degree measure
of A in terms of x ?
F. (180 – x)
G. (180 – 0.5 x)
H. (180 + 0.5 x)
J. (180 + x)
K. is x
36. In ABC, the sum of the measures of ∠A and
∠B is 47°. What is the measure of ∠C ?
A. 47°
B. 86°
C. 94°
D. 133°
E. 143°
37. In a plane, the distinct lines ⃡ and ⃡ intersect
at A, where A is between C and D. The measure
of BAC is 47°. What is the measure of BAD ?
F. 104
G. 118
H. 124
J. 146
K. 152
A. 043°
B. 047°
C. 094°
D. 133°
E. 137°
34. In the figure is below, ̅̅̅̅ and ̅̅̅̅ intersect at D.
What is the measure EAD?
38. In the figure below, ̅̅̅̅ //̅̅̅̅ , ̅̅̅̅ bisects BAC,
And ̅̅̅̅ bisects ACD. If the measure of BAC
is 82°, what is the measure of AEC ?
F. 30
G. 47
H. 50•
J. 53•
K. 70•
Mr . Mosaad El Geneady
A. 86°
B. 88°
C. 90°
D. 92°
E. Cannot be determined from the given information
Mo: 01001851053
ACT
7
Geometry
1. In the figure below, ̅̅̅̅ is congruent to ̅̅̅̅ , and
̅̅̅̅ and ̅̅̅̅ intersect ̅̅̅̅ at C. what is the measure
of B?
4. In the figure below, Lines ⃡ and ⃡ are cut by
Transversals ⃡ and ⃡ that intersect at E. Two
angle measure are given, What is the measure of
ABD ?
A. 28
B. 31
C. 62
D. 118
E. 149
F. 110
G. 112
H. 138
J. 144
K. 146
2. In Isosceles PQR shown below, ̅̅̅̅ ̅̅̅̅ and
the measure of P is 54. If it can be determined,
What is the measure of Q ?
5. In the figure is below, line l and line m are
parallel. line a and line b are intersect line l
at the same point. What is the value of x?
Section (2)
F. 36
G. 54
H. 72•
J. 81•
K. Cannot be determined from the given information
3. In the figure below, ̅̅̅̅// ̅̅̅̅ , A measure 41,
C measure 110and ADB measure 122.
What is the measure of CBD ?
A. 17
B. 41
C. 53
D. 63
E. 6
Mr . Mosaad El Geneady
A. 6
B. 11
C. 14
D. 18
E. 30
6. In the figure is below, ⃡ is parallel to ⃡ , B lies
on ⃡ and ⃡ , F lies on ⃡ , the measure of
ABC is 132, and EBG GBF FBD.
What is the measure of BFD?
A. 84
B. 86
C. 88
D. 89
E. 92
Mo: 01001851053
8
ACT
Geometry
Use the following information to answer questions 10 - 12.
In the parallelogram ABCD shown below, the
diagonals intersect at E, mBDC = 42,
mBDA = 71, and AB = (
) inches
x
l
35 m
60
k
s
t
7. In the figure below, line l is parallel to line m and
line k is parallel to line s. What is the value of x?
10. What is mBAD?
A. 65°
B. 80°
C. 85°
D. 95°
E. 115°
A. 23
B. 42
C. 48
11. Given that DC = (
value of n?
8. In the figure s below, parallel lines a and b
intersect parallel lines c and d. If it can be
determined, what is the sum of measure of
1 and 2?
F. 2
G. 4
E. 71
) inches, what is the
H. 6
J. 12
K. 36
12. Suppose A and B are located at (2,10) and (30,3),
What is the coordinates of E
A. (
B. (
F. 220
G. 180
H. 140•
J. 110•
K. Cannot be determined from the given information
D. 67
)
)
C. (
D. (
E. (
)
)
)
13. In parallelogram ABCD, ̅̅̅̅ is a diagonal . the
measure of ABC is 40, and the measure of
ACD is 57. What is the measure of CAD ?
9. In triangle ABC in the figure above, x = 89.
What is the value of y?
A) 8
B) 10
C) 13
D) 16
Mr . Mosaad El Geneady
E) 19
A. 40
B. 57
C. 77
D. 83
E. 97
Mo: 01001851053
ACT
14. In the figure below, ̅̅̅̅ and ̅̅̅̅ intersect at C,
and ̅̅̅̅ //̅̅̅̅ . Which of the following angles
must have the same measure as BAC ?
F. ACB
G. ACD
H. BCE
J. CDE
K. CED
15. Lines a, b, c, and d are shown below and a // b.
Which of the following is the set of all angles
that must be supplementary to ∠x ?
9
Geometry
18. In the figure below, line l is parallel to line m.
Transversals t and u intersect at point A on l and
intersect m at points C and B, respectively. Point
X is on m, the measure of ∠ ACX is 130°, and the
measure of ∠ BAC is 80°. How many of the angles
formed by rays of l, m, t,and u have measure 50° ?
A. 4
B. 6
C. 8
D. 10
E. 12
19. For the triangles in the figure below, which of
the following ratios of side lengths is equivalent
to the ratio of the perimeter of ABC to the
perimeter of DAB ?
F. {1, 2}
G. {1, 2, 5, 6}
H. {1, 2, 9, 10}
J. {1, 2, 5, 6, 9, 10}
K. {1, 2, 5, 6, 9, 10, 13, 14}
16. In the figure below, B lies on ̅̅̅̅ , ̅̅̅̅ bisects
ABE, and ̅̅̅̅ bisects CBD. What is the
measure of DBE ?
A. 90°
B. 60°
C. 45°
D. 30°
E. Cannot be determined from the given information
17. In isosceles trapezoid ABCD, ̅̅̅̅ is parallel to
̅̅̅̅ DC, BDC measures 25°, and BCA
measures 35°. What is the measure of DBC ?
F. AB:AD
G. AB:BD
H. AD:BD
J. BC:AD
K. BC:BD
20. In right triangle ACD shown below, B lies on
Side ̅̅̅̅ . Some angle measures are given.
What is the measure of BDC ?
A. 25°
B. 35°
C. 50°
D. 55°
E. 60°
A. 85°
B. 95°
C. 105°
D. 115°
E. 125°
Mr . Mosaad El Geneady
Mo: 01001851053
10
ACT
21. In the figure below, ̅̅̅̅, ̅̅̅̅ , and ̅̅̅̅ all
intersect at point Z. the measure of 2 angles are
given. What is the measure of CZE ?
Geometry
24. In the figure below, lines l and m are parallel,
Line n is a transversal, and 3 angle measure are
Given. What is the value of x – y ?
x
l
y
50
A. 76
B. 102
C. 104
D. 119
E. 129
F.
G.
H.
J.
K.
22. In the figure below. line is parallel to line m.
What is the measure of BOD?
B
A
35
D
m
A. 35
B. 75
C. 85°
D. 105°
E. 145°
23. In the figure above, what is the value of x ?
A.
B.
C.
D.
E.
B
A
140
C
25. Triangle ABC, the measure of A is 43,
the measure of BAC is (4y), and the measure
of BCD is (11y). What is the measure of B?
l
O
18
20
16
14
22
Mr . Mosaad El Geneady
m
–80
50
80
130
180
43
A. 12°
B. 48°
C. 89°
D. 91°
E. 132°
(4y)
(11y)
C
D
26. In parallelogram ABCD below, the measure of
BCD is 38, What is the measure of BDA?
A.
B.
C.
D.
E.
38°
41°
44°
49°
52°
Mo: 01001851053
11
ACT
27. In the figure below, ̅̅̅̅ = ̅ , the measure of
ABC is 80, the measure of ADC is 100,
What is the measure of BAC?
Geometry
30. In the figure below, A is on ⃡ and C is on ⃡
What is the measure of ABC ?
.
A. 24
B. 42
C. 45
D. 48
E. 66
A.
B.
C.
D.
E.
80°
100°
120°
60°
70°
31. In the figure is below, ̅̅̅̅ and ̅̅̅̅ intersect at D.
What is the measure EAD?
28. In right triangle ACD shown below, B lies on
Side ̅̅̅̅ . Some angle measures are given.
What is the measure of BDC ?
A. 25°
B. 35°
C. 50°
D. 55°
E. 60°
F. 30
G. 47
H. 50
J. 53
K. 70
29. In the figure below, ̅̅̅̅ is congruent to ̅̅̅̅ , and
̅̅̅̅ and ̅̅̅̅ intersect ̅̅̅̅ at C. what is the measure
of B?
32. In any parallelogram ABCD, it is always true
that the measures of ∠ABC and ∠BCD:
A. 28
B. 31
C. 62
D. 118
E. 149
F. add up to 180°.
G. add up to 90°.
H. are each greater than 90°.
J. are each 90°.
K. are each less than 90°.
Ans:F
33. In ABCD , A measure greater than 43 and
A measure exactly 90. Which of the following
phrases best describes the measure of C ?
A. Greater than 47
B. Equal to 47
C. Equal to 60
D. Equal to 133
E. Less than 7
Mr . Mosaad El Geneady
Mo: 01001851053
ACT
34. What is the measure of the smaller angles formed
by the line and the ray shown in the figure below
A. 14
B. 28
C. 29
D. 58
E. Cannot be determined from the given information
35. Marie is building a kite. In a drawing of her kite,
shown below, AB = BC, AD = DC, The measure
of ABC is 48, and the measure of ADC is 50,
What is the of BAD ?
A. 50
B. 65
C. 90
D. 115
E. 130
36. In the figure below, ̅̅̅̅ is perpendicular to ̅̅̅̅ ,
is perpendicular to ̅̅̅̅ , and ̅̅̅̅ ̅̅̅̅ . Which
of the following congruences is NOT necessarily
true?
F. ̅̅̅̅ ̅̅̅̅
G. ̅̅̅̅ ̅̅̅̅
H. ̅̅̅̅ ̅̅̅̅
J. DAB CBA
K. AB EBA
Mr . Mosaad El Geneady
12
Geometry
37. In the figure below, A, D, B, and G are collinear.
If CAD measures 76°, BCD measures 47°,
and CBG measures 140°, what is the degree
measure of ACD ?
F. 12°
G. 14°
H. 17°
J. 36°
K. 43°
38. In the figure below, A, B,C, and E are
collinear. and ̅̅̅̅, ̅̅̅̅ , and ̅̅̅̅ are all the same
length, and angle ABD is as marked. What
is the measure of BCE?
F. 50
G. 100
H. 105
J. 130
K. 160
39. A rectangle has an area of 32 square feet and a
perimeter of 24 feet. What is the shortest of the
side lengths, in feet, of the rectangle?
F. 1
G. 2
H. 3
J. 4
K. 8
40. If ∠A and ∠B are acute angles, then ∠A and ∠B
CANNOT be
(A) vertical angles
(B) complementary angles
(C) supplementary angles
(D) congruent angles
(E) adjacent angles
Mo: 01001851053
ACT
13
Geometry
41. The measure of QOR is 140, the measure of
3 angles are given in term of x. What is the
measure of QOS ?
F. 96
G. 100
H. 120•
J. 138•
K. 140 •
42. In ABC below, D,E, and F are points on ̅̅̅̅ ,
̅̅̅̅ and ̅̅̅̅ . ̅̅̅̅ ̅̅̅̅ . What is the sum of
measures of the angles marked x and y?
F. 40
G. 80
H. 90•
J. 100•
K. 130 •
45. In Figure 9, points A, B, C, and D are all on the
circle with center O. If BDA measures 25°,
and ∠CAD measures 32°, what is the measure of
BOC in degrees?
A. 33
B. 66
C. 123
D. 147
E. 303
46. In ABC below, points A, C, E, and G are
collinear; and D, E, and F are collinear. What
is the measure of EFG?
A. 40
B. 45
C. 60
D. 80
E. Cannot be determined from the given information
47. What is the measure of each exterior angle of a
regular pentagon?
44. In Figure 4, WX WZ and XY ZY . n
A. 50
B. 142
C. 25
D. 26
E. 168
Mr . Mosaad El Geneady
(A) 90
(B) 60
(C) 120
(D) 108
(E) 72
48. How many lines of symmetry does a rhombus have?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Mo: 01001851053
ACT
Section (3)
1. Shown below are similar triangles ABC and
DEF with A D and B E. The given
Lengths are in inches. What is the length of ̅̅̅̅ ?
A. 3
B. 4
C. 4
D. 5
14
Geometry
4. In the figure below, ABC and DEF are similar
triangles. What is the perimeter of DEF?
A. 3
B. 8
C. 11
D. 12
E. 13
5. In the figure below, E is on ̅̅̅̅ and C is on ̅̅̅̅.
What is the length of ̅̅̅̅?
E. 6
2. Shown below are right triangles ACD and
ABE with lengths given in inches.
What is the length of ̅̅̅̅ ?
A. 5
B. 5
F. 2,640
G. 2,784
H. 3,960
J. 4.400
K. 5,840
C. 5
D. 6
E. 8
3. In right triangle ADE shown below, ̅̅̅̅ // ̅̅̅̅
What is the length of ̅̅̅̅ ?
6. In right triangle ACE below,
is parallel
to
, and
is perpendicular to
at D. The
length of
is 20 feet, the length of
is 3 feet,
and the length of
is 4 feet. What is the length,
in feet, of
?
A.
B.
C.
D. 3
E. 5
Mr . Mosaad El Geneady
A. 10
B. 12
C. 15
D. 16
E. 17
Mo: 01001851053
15
ACT
7. Surveyors want to determine a pond`s length,
represented by ̅̅̅̅ in the figure below. They
place stakes at points A, B, C,D, and E so that
C is the intersection of ̅̅̅̅ and ̅̅̅̅ and so that
̅̅̅̅ is parallel to ̅̅̅̅ . The distances between
certain stakes are shown in the figure. What is
the pond`s length, in meter?
F.
G.
H.
J.
K.
46
52
56
62
67
8. In the figure shown below, ̅̅̅̅ // ̅̅̅̅ , BD = AD,
D and E are on ̅̅̅̅ and ̅̅̅̅ , respectively, AC = 8ft
And the height of ABC is 10 ft. What is DE, in ft?
F.
G.
H.
J.
K.
Geometry
9. Lines l1 and l2 intersect each other and 3 parallel
Lines, l3, l4, and l5,at the points shown in the
figure below. The ratio of the perimeter of
ABC to the perimeter of AFG is 1:3. The ratio
DE to FG is 2:3. What is the ratio AC to CE?
F. 1:1
G. 1:2
H. 1:3
J. 2:1
K. 3:1
10. The triangles below are similar ( ABC DEF)
Which of the following is an expression for the
area of ABC?
2
3
4
5
6
F. (
)(
)
G. ( )( )
H. ( )( )( )
9. In the figure above, ABC is similar to DEF
What is the value of y?
A. 3
B. 4
C. 4.5
D. 5
E. 6
Mr . Mosaad El Geneady
J. ( ) ( )
K. ( )( )
Mo: 01001851053
ACT
11. Marisa`s design for a rectangle stained glass
window with 7 triangles is shown below. The
2 white triangles are congruent ( ABC DEC)
What is the measure of CED?
A. 45°
B. 65°
C. 70°
D. 115°
E. 135°
12. In the figure above, ABC and DEF are similar.
What is the length of DF?
A. 3
B.
C.
D. 7
E.
13. In the figure shown below, ABC DEF, sides
̅̅̅̅ and ̅̅̅̅ are 7.2 cm long, side ̅̅̅̅ is 10.8 cm
the measure of E is 42. What is the measure
of C ?
A. 42
B. 46
C. 60
D. 63
E. 69
Mr . Mosaad El Geneady
16
Geometry
14. Given the 2 similar right triangles shown below
with dimension given in inches, What is the
area of the smaller triangle?
A. 1
B. 3
C. 4
D. 6
E. 12
15. In the figure shown below, E and G lie on ̅̅̅̅ ,
D and F lie on ̅̅̅̅ , ̅̅̅̅ and ̅̅̅̅ are parallel to ̅̅̅̅ ,
What is the length of ̅̅̅̅ ?
A. 9
B. 18
C. 21
D. 30
E. 36
16. In the figure shown below, ABC DEF, sides
̅̅̅̅ and ̅̅̅̅ are each 7.2 cm long, side ⃡ is
10.8cm long, and the measure of E is 42.
What is the measure C ?
A. 42
B. 46
C. 60
D. 63
E. 69
Mo: 01001851053
17
ACT
Geometry
17. In the figure below, ̅̅̅̅ is parallel to ̅̅̅̅, E is
the midpoint of ̅̅̅̅. F is the midpoint of ̅̅̅̅ .
G is the midpoint of ̅̅̅̅ , and H is the midpoint
of ̅̅̅̅ . The lengths marked are in inches. What
is the length of ⃡ , in inches?
20. In the figure above, ABE is similar to ACD.
What is the value of x?
F. 31
G. 31
H. 37
J. 38
K. 43
(A) 3
(B) 3.5
(C) 3.75
(D) 4
(E) 13.75
18. In the figure is shown below, ̅̅̅̅ // ̅̅̅̅ , ̅̅̅̅
and ̅̅̅̅ intersect at B. what is the length of ̅̅̅̅ ?
21. In right triangle ABC, ̅̅̅̅
̅̅̅̅ . If AB = 6,
AC = 8, BC = 10, and DE = 4, find EC.
A.
B.
C. 5
D. 6
E.
F.
G.
H.
J.
K.
6
8
9
10
11
19. The ratio of the side lengths for a triangle is
exactly 12:14:15. In a second triangle similar to
the first, the shortest side is 8 inches long. To
nearest tenth of an inch, what is the length of
the longest side of the second triangle
22. Two triangles are similar. The shortest side of the
smaller triangle is 9 inches long, and the shortest
side of the larger triangle is 16 inches long. The
perimeter of the smaller triangle is 36 inches.
What is the perimeter of the larger triangle?
F. 43
G. 48
H. 57
J. 61
K. 64
A. 11.0
B. 10.0
C. 9.3
D. 6.4
E. Cannot be determined from the given information
Mr . Mosaad El Geneady
Mo: 01001851053
ACT
23. Points B and C lie on ̅̅̅̅as shown below. The
length of ̅̅̅̅ is 30 units; ̅̅̅̅ is 16 units long; and
̅̅̅̅ is 220 units long, How many unit long if it
can be determine, is ̅̅̅̅ ?
F. 4
G. 6
H. 10
J. 14•
K. Cannot be determined from the given information
24. As shown below, A, B, C, and D are collinear,
with B between A and C, and with C between B
and D. Given AC = BD = 12cm and given
BC = 3cm, what is the length of AD?
18
Geometry
26. What is the maximum number of distinct
diagonals that can be drawn in the hexagon
shown below?
A. 4
B. 5
C. 6
D. 9
E. 12
27. Shown below is a regular hexagon inscribed in a
circle whose radius is 4 inches. What is the
perimeter of the hexagon?
A. 8
B. 12√
C. 18
D. 20
E. 24
F. 9
G. 15
H. 18
J. 21
K. 27
28. Shown below is a regular hexagon inscribed in a
circle whose radius is 4 inches. What is the
perimeter of the hexagon?
25. In pentagon ABCDE, shown below, A measures
50.What is the total measure of the other
4 interior angles?
F. 30
G. 30√
H. 60
J. 60√
K. 60√
29. What is the measure of each exterior angle of a
regular pentagon?
F. 130
G. 200
H. 310•
J. 432•
K. 490•
Mr . Mosaad El Geneady
A. 90
B. 60
C. 120
D. 108
E. 72
Mo: 01001851053
ACT
30. In the figure below, the measure of 4 angles of
pentagon ABCDE are given, What is the measure
of A?
A. 100
B. 108
C. 120
D. 140
E. 160
31. The measure of interior angles of a pentagon are
70, 100, 110 and 135, respectively. What is
The measure of the 5th interior angle?
F. 35
G. 55
H. 83
J. 108
K. 125
32. The degree measures of the interior angles of a
certain pentagon are in ratio 2:3:4:4:5. What is
the measure of the last interior angle of this
pentagon?
A. 30
B. 60
C. 90
D. 120
E. 150
19
Geometry
34. How many sides does a regular polygon have if
Each interior angle measures 140?
A. 6
B. 7
C. 8
D. 9
E. 10
35. Five points are shown on each of the 2lines in the
figure below. Point O is the intersection point of
the 2 lines. Which of the following rays does NOT
contain point O?
F.
G.
H.
J.
K.
36. In the regular heptagon shown below, what is
The sum of the measures of the 7 interior angles?
F. 360
G. 720
H. 900
J. 1,080
K. 1,260
33. All six sides of the polygon shown below
are congruent. What is the value of x?
37. The midpoints of the sides of rectangle WXYZ are
vertices of rhombus ABCD . The dimensions of
rectangle WXYZ are 6cm by 8cm. What is the
perimeter of rhombus ABCD ?
A. 258
B. 240
C. 220
D. 180
E. 165
F.
G.
H.
J.
K.
Mr . Mosaad El Geneady
20
25
28
40
36
Mo: 01001851053
20
ACT
Section (4)
1. A parallelogram ABCD shown below. What is the
area of the parallelogram
Geometry
4. In the figure shown below, ̅̅̅̅ ̅̅̅̅, and
rectangle ABCD has a length of 6 inches and
a width of 4 inches. The area of rectangle EFGD
is 2 times the area of rectangle ABCD. What is
the length of ̅̅̅̅
F
G
4
A. 18
B. 36
C. 39
D. 45
E. 72
2. What is the perimeter, in feet, of the figure
shown below?
8 ft
20 ft
C
6
F.
G.
H.
J.
K.
D
A
E
2
2.4
3.5
4
4.8
5. A square is circumscribed about a circle of 7 cm
radius. What is the area of square?
14 ft
20 ft
A.
B.
C.
D.
E.
60
62
70
80
8
3. The figure shown below, all angles are right
angles, and the sides lengths are in yards. What
is the area of the figure?
F. 49
G. 56
H. 98
J. 49
K.196
B
C
9
4
150
10
A
6
D
4
F. 12
G. 74
H. 98
J. 110
K. 134
11
Mr . Mosaad El Geneady
6. The area of parallelogram ABCD above is
A. 12
B. 20
C. √
D.
√
E. 24
Mo: 01001851053
21
ACT
Geometry
7. What is the area of the parallelogram shown
below
6 in
13
8
5 in
20
10 in
A. 42
B. 50
C. 55
D. 60
E. 75
8
10. A corner is cut from a rectangular sheer of paper
to produce the pentagon shown in the figure
above. What is the perimeter of the pentagon ?
8. The figure shown below, all angles are right
angles, and the sides lengths are in yards.
What is the area of the figure?
A. 49
B. 52
C. 61
D. 62
E. 76
6
11. In the figure below is composed of a square
BCDE and equilateral triangle ABE. The
length of ̅̅̅̅ is 6 inches. What is the perimeter
of ABCDE ?
9
3
13
F. 42
G. 75
H. 93
J. 99
K. 117
9. If the area of KLMN in the figure below is 12cm2,
What is the length of ̅̅̅̅ ?
K
5 cm
12. The figure shown below, all angles are right
angles, and the sides lengths are in yards.
What is the area of the figure?
45
F.
G.
H.
J.
K.
2√
5√
6√
2√
√
Mr . Mosaad El Geneady
18
24
30
42
45
L
?
N
A.
B.
C.
D.
E.
M
F. 49
G. 71
H. 86
J. 105
K. 120
Mo: 01001851053
22
ACT
13. The interior of a rectangular shipping crate has
dimensions 2ft by 3ft by 6ft. The crate will be
filled with cube-shaped boxes whose exteriors
have dimensions 12in by 12in by 12in. Given that
no box can extend beyond the dimensions of the
crate1s interior, what is the maximum number of
boxes the cart can hold?
A. 3
B. 12
C. 36
D. 48
E. 72
14. A rectangular solid has a volume of 100 cubic
units, If the length, width, and height of the solid
are each doubled, what will be the volume of the
new solid be?
Geometry
17. The length of hypotenuse of a certain right
triangle is 50 inches, and the length of one of its
leg is 40 inches. What is the length of the other
leg of the triangle
F.
G.
H.
J.
K.
10
30
45
64
90
18. The floor plan oh Helena`s kitchen is shown in
the figure below; the given dimensions are in
feet, Helena will install baseboard along the
bottom of each wall ( shown by solid lines in
the floor plan). According to the floor plan,
which of the following distances is closest to
the perimeter of Helena`s kitchen?
10
F. 200
G. 400
H. 600
J. 800
K. 2,700
15. The ratio of the radii of 2 circles is 4:9. What is
the ratio of their circumferences?
F. 2 : 3
G. 4 : 9
H. 16 : 81
J. 4 : 8
K. 9 : 18
16.
All of the following statements concern
triangles that are similar, congruent, or both.
Which statement is FALSE?
A. Triangles that are congruent are always similar
B. Lengths of corresponding sides of similar
triangles are always equal.
C. Lengths of corresponding sides of congruent
triangles are always equal.
D. Measure of corresponding angles of similar
triangles are always equal.
E. Measure of corresponding angles of congruent
triangles are always equal
Mr . Mosaad El Geneady
8
19
F. 40
G. 50
H. 60
J. 100
K. 120
19. In the figure below, the area of the larger square
is 50 square centimeters and the area of the
smaller square is 18 square centimeters.
What is x, in centimeters?
F. 2
G. 2√
H. 4√
J. 16
K. 32
Mo: 01001851053
23
ACT
20. In the 8-sided figure below, adjacent sides meet
at right angles and the lengths given are in meters.
What is the perimeter of the figure, in meters?
Geometry
23. In the figure is below, E lies on ̅̅̅̅ . The area
of AED is what fraction of area of rectangle
ABCD ?
8
12
20
A.
A. 40
B. 80
C. 120
D. 160
E. 400
B.
C.
D.
E.
21. Roger will pour concrete to make a sidewalk with
the dimensions in feet, shown in the figure below.
He will pour the concrete to a depth of 4 inches.
One bag of concrete mix makes 0.6 cubic feet of
concrete. What is the least whole number of bags
of concrete mix that Roger needs in order to
make the sidewalk?
F.
G.
H.
J.
K.
20. What is the area of the figure below ?
F.
G.
H.
J.
K.
16
44
50
58
67
60
80
275
375
450
21. In the figure below, what is the perimeter of the
Figure below?
3
22. In the figure is shown below, all angles are right
Angles, and the lengths given in meters. What is
The area of the figure?
2
7
1
8
4
F.
G.
H.
J.
K.
12
52
68
80
96
10
Mr . Mosaad El Geneady
4
A. 10
B. 12
C. 13
D. 14
E. 16
Mo: 01001851053
ACT
22. The base length of isosceles trapezoid ABCD
shown below, and E is on ̅̅̅̅ . What is the
ratio of area of ABCD to the area of AED?
A. 2 : 1
B. 4 : 1
C. 5 : 1
D. 10 : 1
E. 20 : 1
23. In quadrilateral ABCD shown below, ̅̅̅̅ // ̅̅̅̅,
BC = 20 inches, AD = 28 inches, and the
distance between ̅̅̅̅ and ̅̅̅̅ is 7 inches. What
is the area of quadrilateral ABCD?
A. 140
B. 168
C. 196
D. 336
E. 560
24
Geometry
25. A rectangle that is c inches by d inches is in the
interior of a rectangle that is a inches by b inches.
As shown below. The area of the shaded region is
What fraction of the area of the large rectangle,
In term of a, b, c, and d ?
A.
B.
C.
D.
E.
(
)(
)
26. Squares with sides of length x cm have been
removed from each corner of a rectangle
measuring 8 cm by 18 cm, resulting in the figure
below. In term of x, what is the area of the figure
24. Square ABCD shown below, has a side length of
10 inches. Point D is the midpoint of ̅̅̅̅ and
F is the midpoint of ̅̅̅̅ . What is the ratio of the
area of DEF, shown shaded , to the area of
pentagon ABCDF?
F. 52 – 4x2
G. 144 – 4x2
H. 144 + 4x2
J. 144 – 8x
K. 144 – 52x + 4x2
A. 1: 3
B. 1: 4
C. 1: 7
D. 1: 8
E. 1: 10
Mr . Mosaad El Geneady
27. One side of square ABCD has a length of 18
meters. A certain rectangle whose area is equal
to the area of ABCD has a width of 6 meters.
What is the length of the certain rectangle?
A.
B.
C.
D.
E.
18
24
27
30
54
Mo: 01001851053
25
ACT
28. A square has a perimeter of 20 feet. What is the
Area of the square?
F. 5
G. 10
H. 25
J. 40
K. 80
29. The sides lengths of a certain triangle are 4, 6, 7
Which of the following descriptions best
classified this triangle ?
F. Scalene acute
G. Scalene right
H. Scalene obtuse
J. Isosceles obtuse
K. Isosceles right
Geometry
32. The perimeter of 1 of the 25 congruent squares is
how many meters?
F.
G.
H.
J.
K.
1
4
5
20
25
34. The lengths of corresponding sides of 2 similar
right triangles are in ratio 2:9. The hypotenuse of
the smaller triangle is 8 inches long. How many
inches long is the hypotenuse of the larger
triangle ?
F.
G.
H.
J.
K.
4.5
11
15
18
36
30. In the figure below shows 12 congruent line
segments, each determined by a pair of adjacent
points. The sum of the lengths of the 12 line
segments is 36 cm. Each intersection of 4 of the
line segments forms 4 right angles. What is the
area of the shaded region?
35. For ABC shown below, base ̅̅̅̅ has a length of
16 inches and altitude ̅̅̅̅ has a length of 8 inches
The area of a certain square is equal to the area of
ABC. What is the length of side of the square?
A. 4
B. 6
C. 9
D. 12
E. 16
F. 6
G. 8
H. 12
J. 16
K. 32
31. The dimension of equilateral triangle ABC are
given in the figure below. What is the value of y?
36. The lengths of 2 legs of right triangle ABC
shown below . The midpoint of ̅̅̅̅ is how many
inches from A?
F.
G.
H.
J.
K.
A. 16
B. 20
C. 21
D. 28
E. 40
2
5
8
13
16
Mr . Mosaad El Geneady
Mo: 01001851053
26
ACT
Geometry
Section (5)
1. In square ABCE shown below, D is the midpoint
of ̅̅̅̅ . Which of the following is the ratio of the
area of ADE to the area of ADB ?
Use the following information to answer questions 5-9 .
In the figure is shown below, ABCD is a rectangle,
EFGH is a square, and ̅̅̅̅ is a diameter of a
semicircle . Point K is the midpoint of ̅̅̅̅ . Point J
is the midpoint of both ̅̅̅̅ and ̅̅̅̅ . Points E and F
lie on ̅̅̅̅ .
F. 1:1
G. 1:2
H. 1:3
J. 1:4
K. 1:8
2. In DEF, the length of ̅̅̅̅ is √ cm, and the
length of ̅̅̅̅ is 3 cm, What is length of ̅̅̅̅ ?
F.
G.
H.
J.
K.
3
√
√
√
Cannot be determined from the given information
3. Laura plane to paint the 8-foot-high rectangular
walls of her room, and before she buys paint she
needs to know the area of the wall surface to be
painted. Two walls are 10 feet wide, and the
other 2 walls are 15 feet wide. The combined
area of the 1 window and the 1 door in her room
is 60 square feet. What is the area of the wall
surface Laura plane to paint ?
A. 200
B. 340
C. 360
D. 390
E. 400
5. The length of ̅̅̅̅ is what percent of the length
of ̅̅̅̅?
A. 15.6%
B. 30%
C. 36%
D. 43.2%
E. 50%
6. What is the length of ̅̅̅ ?
F. 13
G. 15.6
H. 17 J. √
K. √
7. What is the length of arc ̂ ?
A. 2.5 B. 5 C. 6.25 D. 10 E. 25
4. The edges of a cube are each 3 inches long.
What is the surface area, in square inches,
of this cube?
F. 9
G. 18
H. 27
J. 36
K. 54
Mr . Mosaad El Geneady
8. The figure will be placed in the standard (x,y)
coordinate plane so that K is at origin, ̅̅̅̅ is
parallel to the x-axis, and 1 meter equal
1 coordinate unit. Which of the following values
could be the y-coordinate of H?
F. 1.8
G. 3.6
H. 8.4
J. 10
K. 12
Mo: 01001851053
27
ACT
9. In the figure below, the border of a pool and the
border of a patio surrounding that pool are
similar rectangles. What is the length of the pool ?
Geometry
13. The empty container shown below is a right
rectangular prism with dimensions given in
inches. How many cubic inches of liquid are
needed to fill the container to 75% of its capacity
F.
G.
H.
J.
K.
A. 30
B. 40
C. 42
D. 48
E. 52
10. In the figure below, 2 nonadjacent sides of a
regular pentagon (5 congruent sides and 5
congruent interior angles) are extended until
they meet at point X. What is the measure of ∠ X
A. 18°
B. 30°
C. 36°
D. 45
E. 72
148
240
444
720
960
14. The length of a rectangle is 4 inches longer than
the width. The perimeter of the rectangle is
28 inches. What is the width of the rectangle?
A. 5
B. 7
C. 10
D. 12
E. 14
15. A right prism with triangular bases and with
dimensions given in inches is shown below.
What is the prism`s total surface area ?
11. The perimeter of parallelogram is 80 inches, and
The length of 1 side is 18 inches, If it can be
determined, what are the lengths of other 3 sides?
F.
G.
H.
J.
K.
18, 13, 13
18, 18, 26
18, 22, 22
18, 31, 31
Cannot be determined, from the given information
12. Distinct line l and m intersect, forming 4 pairs
of adjacent angles. Which of the following
statements must be true about these 4 pairs
of angles?
F. The difference of the angle measures in each
pair is less than 45
G. The difference of the angle measures in each
pair 90
H. The measures of each angle in each pair is 45
J. The sum of angle measures in each pair is 90
K. The sum of angle measures in each pair is 180
Mr . Mosaad El Geneady
F.
G.
H.
J.
K.
120
204
228
240
264
16. How long, in centimeters, is 1 side of a square
Whose perimeter is equal to the circumference
Of a circle with radius od 2 centimeters?
A.
B.
C. 4
D. 16
E. 4
Mo: 01001851053
28
ACT
17. The line below contain X,Y and Z, in that order.
The ratio of the length of ̅̅̅̅ to the length of ̅̅̅̅
Is 5:9. If it can be determined, what is the ratio
of the length of ̅̅̅̅ to the length of ̅̅̅̅?
Geometry
20. A-foot-wide brick sidewalk is laid around a
rectangular swimming pool. The outside edge of
the sidewalk measures 30 feet by 40 feet, as
shown in the figure below. What is the perimeter,
in feet, of the swimming pool?
A. 5: 14
B. 5: 4
C. 9: 5
D. 14: 5
E. Cannot be determined from the given information
18. In ABC below, D is the midpoint of ̅̅̅̅, BAC
is a right angle, AB = 8m and AC = 10m.
What is AD, in meters?
F. √
G. √
H. √
J. √
K. √
19. In the diagram below, B, F, and H are on ̅̅̅̅ ,
̅̅̅̅ , and ̅̅̅̅ , respectively, and ̅̅̅̅ ̅̅̅̅. The
area of square ABGF is the area of square ACDE.
What percent of the area of ACDE does the shaded
Portion represent?
A. 0.0625%
B. 0.125%
C. 0.25%
D. 6.25%
E. 12.5%
Mr . Mosaad El Geneady
A. 70
B. 116
C. 140
D. 816
E. 1,200
21. A circle has a circumference √ feet. What is
the area, in square feet, of the circle?
A.
B.
C.
D.
E.
√
√
22. The height and radius of the right circular
cylinder below are given in meters. What is the
volume of the cylinder ?
A. 30π
B. 31π
C. 150 π
D. 180π
E. 900π
Mo: 01001851053
29
ACT
Geometry
23. What is the volume of a right circular cone with
radius 3 inches and height 6 inches?
( Note : the volume of right circular cone with
radius r and height h is
)
26. The volume of a sphere is
, where r is the
radius of the sphere. What is the volume of a
sphere with diameter 4 yards?
A. 6
B. 12
C. 18
D. 27
E. 36
F.
G.
H. 32
J. 48
K.
24. A cube with edges 4 cm long is inscribed in a
sphere, as shown below. What is the radius of
the sphere in centimeter?
F.
G.
H.
J.
K.
2√
2√
4√
4√
2
25. The figure below shows a solid concrete ramp for
skateboarding. The length is 10 feet, the width is
6 feet, and the height is 3 feet. Which of the
following values id closest to the volume in
cubic feet, of the concrete used to construct thr
ramp?
27. A father and his son are standing near to each
other on level ground late one afternoon so that
their shadows end at the same place. The father is
75 inches tall, the son is 50 inches tall, and the
The father`s shadow is 120 inches long, as shown
in figure below. Which of the following is
closest to the distance, d inches, between the
father and his son?
F.
G.
H.
J.
K.
25
40
60
70
80
28. To nearest 1 foot, what is the height of
rectangular prism with base length of 15 feet,
and base width 1 feet, and a volume of 100
cubic feet?
F.
G.
H.
J.
K.
5
7
9
20
75
29. The area of a rectangle is 300 square meters, and
its length is 3 times its width. How many meters
wide is the rectangle?
F. 32
G. 76
H. 90
J. 115
K. 180
Mr . Mosaad El Geneady
F. 10
G. 30
H. 50
J. 100
K. 150
Mo: 01001851053
30
ACT
30. The angle measure of CDE are shown below,
Point B lie on ̅̅̅̅, and point C lie on ̅̅̅̅ .
What is the value of cos( + )?
Geometry
34. Kamini is constracting the kite shown below. The
kite include 2 perpendicular supports, one of
length 40 inches and the other of length 28 inches
The ends of the supports are connected with string
to form 4-sided figure that is symmetric with
respect to the longer support. A layer of paper
will cover the interior of the 4-sided figure. Which
of the following is closest to the area that Kamini
will cover with paper?
F. 0
G.
H.
√
√
J.
K. 1
A. 101
B. 280
C. 560
D. 840
E. 980
31. A formula of the volume ,V, of a right circular
cylinder is V = r2h, where r is the radius and h is
the height. The cylindrical tank shown below has
radius 6 meters and height 5 meters and is filled
with water.
35. An 8 inch by – 6-inch rectangle is cut along a
diagonal to form 2 triangles. What is the area
of each triangle?
Given that the weight of 1 cubic meter of water is
approximately 2,205 pound, the weight, in pounds,
of the water in the tank is:
36. Two sides of a triangle are equal of length. The
third side is 3 cm longer than either of the other
2 sides. Given that the perimeter of the triangle
is 93 cm, what is the length of the longest side?
F. less than 400,000.
G. between 400,000 and 900,000.
H. between 900,000 and 1,200,000.
J. between 1,200,000 and 1,700,000.
K. more than 1,700,000.
32. Two concentric circles have radii of 5 centimeters
and 6 centimeters, respectively. How many
centimeters longer is the circumference of the
larger circle than that of the smaller circle
A. 1
B.
C. 2
D. 11
E. 22
Mr . Mosaad El Geneady
F. 7
G. 12
H. 14
J. 24
K. 48
Ans:J
A.
B.
C.
D.
E.
29
30
31
33
34
37. What is the area of a right triangle with side
Lengths 10cm, 26cm, and 24cm?
A. 432
B. 312
C. 260
D. 240
E. 120
Mo: 01001851053
31
ACT
Geometry
Section (6)
1. The rectangle shown in the figure shown below is
partitioned into 3 triangles, 2 of which are shaded
What is the total area of the 2 shaded regions
5. In the figure below, QRS is equilateral, side ̅̅̅̅
is bisected by T, and side ̅̅̅̅ is bisected by U.
What is the degree measure of TUS?
F.
G.
H.
J.
K.
F. 60
G. 90
H. 120
J. 135
K. 150
20
24
32
40
80
2. A parallelogram has a perimeter of 84 inches, and
1 of its sides is 16 inches, If it can be determined,
What are the lengths of other 3 sides?
F.
G.
H.
J.
K.
16, 16, 36
16, 18, 18
16, 26, 26
16, 34, 34
Cannot be determined from the given information
3. A rectangular box that is foot deep, 2 foot wide,
and 1 foot long has a volume of how many cubic
feet?
F.
G. 1
H. 2
J. 9
K. 81
4. A 3-inch-tall rectangular box with a square base
is constructed to hold a circular pie that has a
diameter of 8 inches. Both are shown below.
What is the volume of the smallest such that it
can hold this pie?
A. 24
B. 64
C. 72
D. 192
E. 512
Mr . Mosaad El Geneady
6. A 5-inch-by-7-inch photograph was cut to fit
exactly into 4-inch-by-6-inch frame. What is the
area of part of the photograph that was cut off ?
A. 2
B. 10
C. 11
D. 12
E. 24
7. The length of a rectangle is 12 feet. The width of
the rectangle is the length. What is the perimeter
of the rectangle ?
F.
G.
H.
J.
K.
18
24
30
36
72
17. The total surface area, T, of any right circular cone
with a radius r and a slant height s, such as the
cone shown below, can be determined by using the
formula T = r2 + rs. If a cone has a 3-inch radius
and a 5-inch slant height, what is total surface area?
F. 18
G. 24
H. 40
J. 75
K. 135
Mo: 01001851053
ACT
Use the following information to answer questions 18-20
The top view and side view of a 40-foot-long
swimming pool are shown in the figure below. all
dimensions given are in feet.
32
Geometry
20. A full lap is 2 times the length of the pool.
Johann swam 5 full laps of the pool in 4
minutes. Which of the following values is
closest to Johann`s average swimming speed,
in feet per minute?
F. 35
G. 45
H. 60
J. 90
K. 120
The top view shows the top rectangular surface of the
Pool and the surrounding rectangular patio. All 4
walls of the pool are vertical and perpendicular to the
top surface. The side view shows a cross section
along the length of the pool. All cross sections
parallel to the side view are congruent. The shallow
end has a constant depth of 4 ft. The deep end has a
constant depth of 9ft. A rectangular surface connects
the shallow and deep ends.
18. What is the area of the patio surrounding the pool?
F. 500
G. 600
H. 900
J. 1,100
K. 1,350
19. Johann put up a fence along the outer edge of the
patio. Given that the material for the fence cost
$12 per foot, what was the total cost of the
material for the fence?
A. $1,020
B. $1,320
C. $1,800
D. $3,040
E. $3,360
Mr . Mosaad El Geneady
21. The side view of the pool is placed in the
standard (x,y) coordinate plane, keeping the
same orientation and scale, such that both
vertical segments showing depth are parallel
to the y-axis. Which of the following values is
closest to the slope of the line segment
connecting the shallow end to the deep end?
A. –0.44
B. –0.63
C. –0.75
D. –1.33
E. –1.60
22. The volume of a right circular cone with radius r
and height h is
, Cones A and B are both
right circular cones. The radius of Cone B is
2 times the radius of cone A. Cone B`s height is
Cones A`s height. Compared to the volume of
Cone A, the volume of Cone B is:
A. The same.
B. as greater.
C. as greater.
D. 2 times as greater
E. 4 times as greater
23. The perimeter of rectangle ABCD is 96 cm. The
ratio of the side lengths AB : BC is 3:5. What is
the length of ̅̅̅̅ ?
A. 6
B. 18
C. 30
D. 36
E. 60
Mo: 01001851053
ACT
24. From point A outside a circle and in the same
plane as the circle, 2 rays are drawn tangent to
the circle with the points of tangency labeled B
and C, respectively. Segment ̅̅̅̅ is then drawn to
form ABC. If A measures 70, what is the
measure of ABC?
F. 70
G. 55
H. 40
J. 35
K. Cannot be determined from the given information
25. A line contain points A, B, C, and D. Point B is
between points A and C. Point D is between
points C and B. which of the following
inequalities must be true about the lengths of
these segments?
F. BC < AB
G. BD < AB
H. BD < CD
J. CD < AB
K. CD < BC
Ans:
26. The perimeter of rectangle ABCE is 96cm. the
ratio of the side lengths AB:BC is 3:5. What is
length of ̅̅̅̅?
A. 6
B. 18
C. 30
D. 36
E. 60
27. Toby wants to find the volume of a solid toy
soldier. He fills a rectangular container 8cm
long, 6cm wide, and 10 cm high with water to
a depth of 4 cm. Toby totally submerges the toy
soldier in the water. The height of the water with
the submerged toy soldier is 6.6 cm. Which of
the following is closest to the volume of the
toy soldier?
A. 125
B. 156
C. 192
D. 208
E. 317
Mr . Mosaad El Geneady
33
Geometry
28. The length of a rectangle is 5 inches longer than
the width . The perimeter of the rectangle is
40 inches. What is the width of the rectangle?
F.
G.
H.
J.
K.
7.5
8
15
16
17.5
29. Each side of square ABCD has a length of 50cm.
A certain rectangle whose area is equal to the
area of ABCD has a width of 10cm. What is the
length of the rectangle
A. 40
B. 50
C. 60
D. 125
E. 250
30. In DEF, the length of ̅̅̅̅ is √ cm, and the
length of ̅̅̅̅ is 6 cm, What is length of ̅̅̅̅ ?
F.
G.
H.
J.
K.
6
√
√
√
Cannot be determined from the given information
31. The length of a rectangle is 5 inches longer than
the width. The perimeter of the rectangle is 40
inches. What is the width of the rectangle ?
F. 07.5
G. 08
H. 15
J. 16
K. 17.5
32. A room has a rectangular floor that is 15 feet by
21 feet. What is the area of the floor in square
yards?
A. 24
B. 35
C. 36
D. 105
E. 144
Mo: 01001851053
ACT
34. The lengths of the legs of a right triangle are
4 miles and 5 miles. Which of the following is
closest to that of the hypotenuse of the right
triangle
F. 3.0
G. 4.5
H. 6.4
J. 12
K. 36
A
35. The parallel sides of the isosceles trapezoid
shown below are 10 feet long and 16 feet long,
What is the distance, between these 2 sides?
A. 3
B. 4
C. 5
D. 10
E. 16
34
Geometry
38. A rectangle has area of 32 square feet and a
perimeter of 24 feet. What is shortest of the
lengths of the rectangle ?
F. 1
G. 2
H. 3
J. 4
K. 8
39. In the figure below, points E and F are the
midpoints of sides
and ̅̅̅̅ of rectangle
ABCD, point G is the intersection of AF and
, and point H is the intersection of
and
. The interior of ABCD except for the interior
of EGFH is shaded. What is the ratio of the area
of EGFH to the area of the shaded region?
36. What is the perimeter, in inches, of the isosceles
right triangle shown below, whose hypotenuse is
8√ inches long?
A. 8
B. 8 + 8√
C. 8 + 16√
D. 16
E. 16 + 8√
37. The length of a rectangle is 3 times the length of
a smaller rectangle. The 2 rectangles have the
same width. The area of the smaller rectangle is a
square units. The area of the larger rectangle is
kA square units. Which of the following is the
value of k ?
F. 1:2
G. 1:3
H. 1:4
J. 1:6
K. Cannot be determined from the given information
40. In the figure below, ABCD is a square. Points are
chosen on each pair of adjacent sides of ABCD to
form 4 congruent right triangles, as shown below.
Each of these has one leg that is twice as long as
the other leg. What fraction of the area of square
ABCD is shaded?
F.
G.
H. 1
J. 3
K. 9
A.
B.
C.
D.
E.
Mr . Mosaad El Geneady
Mo: 01001851053
ACT
35
Geometry
Section (7)
1. What is the surface area, in square inches, of an
8-inch cube?
5. If a rectangle measure 54 meter by 72 meters,
What is the length of the rectangle?
F. 512
G. 384
H. 320
J. 256
K. 192
F. 48
G. 63
H. 90
J. 126
K. 252
2. Triangles _ABC and _PQR are shown below. The
given side lengths are in centimeters. The area of
ABC is 30 square centimeters. What is the area
of PQR, in square centimeters?
6. Parallelogram ABCD, shown below.
What its area?
F. 15
G. 19
H. 25
J. 30
K. 33
3. Which of the following sets of triangle side lengths
Represent a right triangle
A. 1, 2, 5
B. 2, 3, 4
C. 4, 5, 21
D. 5, 12, 13
E. 6. 9. 11
4. In the figure below, ABCE is a square and E,F,G
and H are the midpoints of its sides. If AB = 12cm
what is the perimeter of EFGH ?
A. 18
B. 36
C. 39
D. 45
E. 72
7. The trapezoid below is divided into 2 triangles
and 1 rectangle. What is the combined area of
the 2 shaded triangles?
A. 4
B. 6
C. 9
D. 12
E. 18
8. Point B on ̅̅̅̅ between A and C. Point D is a
point not on ̅̅̅̅ such that the measure of ABD
is 38. What is the measure of CBD?
F. 24
G. 24√
H. 36√
J. 48√
K. 72
Mr . Mosaad El Geneady
A. 38
B. 52
C. 76
D. 128
E. 142
Mo: 01001851053
36
ACT
9. The tent illustrated below is in the shape of a
right triangular prism and is made of nylon. How
many square feet of nylon is required for the
front, rear, and 2 sides of the tent?
F. 47
G. 59
H. 82
J. 94
K. 188
10. In the rhombus ABCD below, ̅̅̅̅ is 8 inches long
and ̅̅̅̅ is 6 inches long. What is the area of ACBD
Geometry
12. What is the circumference of a circle with radius
6cm?
F.
G.
H.
J.
K.
3
9
12
36
13. In the figure is below, parallel lines ⃡ and ⃡
are cut by transversals ⃡ and ⃡ that intersect
at E. What is the measure of ABD ?
F. 110
G. 112
H. 138
J. 144
K. 146
F.
G.
H.
J.
K.
5
24
25
32
48
11. In the figure is below, B,F, and H are on ̅̅̅̅ , ̅̅̅̅ ,
and ̅̅̅̅ , respectively, and ̅̅̅̅ ̅̅̅̅ . The area of
square ABGF is the area of square ACDE. The
the area of FGH is what fraction of the area of
square ACDE.
F.
G.
H.
J.
14. The intersection of lines l and m forms the
4 angles A, B, C, and D. The measure
of B is 3 times the measure of A. which of
the following closest to measure A ?
F. 20
G. 26
H. 35
J. 40
K. 51
15. In ABC shown below, sin C = and the length
of ̅̅̅̅ is 10 inches. What is the length of ̅̅̅̅ ?
A. 3
B. √
C. 8
D. 9
E.
K.
Mr . Mosaad El Geneady
Mo: 01001851053
37
ACT
16. The length of the rectangular prism shown below
is twice the width. The height and the width are
the same. The volume of the prism is 128 cubic
inches . what is the length of the prism?
A. 2
B. 4
C. 8
D. 16
E. 32
17. Each edge of a cube is 4 inch long. Each edge of
a second cube is triple the length of each edge of
the first cube. The volume of the second cube is
how many cubic inches bigger than the volume of
the first cube ?
F. 128
G. 512
H. 576
J. 1,664
K. 1,728
18. The midpoints of the sides of rectangle WXYZ are
vertices of rhombus ABCD . The dimensions of
rectangle WXYZ are 6cm by 8cm. What is the
perimeter of rhombus ABCD ?
F.
G.
H.
J.
K.
20
25
28
40
36
Geometry
20. In the figure is shown below, ̅̅̅̅ divides the
rectangle ACDF into 2 congruent trapezoids.
the measure of BED is 45, ̅̅̅̅ ̅̅̅̅ = 4cm
length of ̅̅̅̅ = 6cm. What is the area of
rectangle ACDF
F.
G.
H.
J.
K.
20
25
28
40
36
21. In the figure below, p is on ̅̅̅̅, and E is on ̅̅̅̅ ,
polygon ABCDEF, with dimensions marked, has
area of 122 square inches. What is the area of
PEB ?
F. 3
G. 6
H. 12
J. 13
K. 15
22. What is the length of side of square whose area
is equal to area of a rectangle 25m by 16m ?
19. In trapezoid ABCD shown below, ̅̅̅̅ is 8cm ,
̅̅̅̅ is 12cm long, and ̅̅̅̅ is 6 cm . AEF and
DFE are right angles. What is the area of the
trapezoid ?
A. 60
B. 72
C. 84
D. 120
E. 288
Mr . Mosaad El Geneady
A. √
B. 42
C. 48
D. 67
E. 71
Mo: 01001851053
38
ACT
23. What is the volume of right circular cylinder
shown below ?
F.
G.
H.
J.
K.
220
310
700
1,540
2,200
24. A swimming pool in the shape of a right
rectangular prism has length 12 feet and width
14 feet. The volume of water in the pool is 2,520ft3.
To nearest foot, what is the depth of water in the
Pool?
F.
G.
H.
J.
K.
7
10
15
24
90
25. In a certain rectangle, the ratio of the lengths of
2 adjacent sides is 5 to 2. If the area of the
rectangle is 90 square inches, what is the length
of the longest side?
A. 6
B. 9
C. 15
D. 18
E. 45
Geometry
27. A formula for the surface area (A) of the
rectangular solid shown below is
A = 2lw + 2lh + 2wh where l represents length;
w, width; and h, height. By doubling each of the
dimensions (l, w, and h), the surface area will be
multiplied by what factor?
A. 02
B. 04
C. 06
D. 08
E. 12
28. The triangle, XYZ, that is shown below has
side lengths of x, y, and z inches and is not a
right triangle. Let X` be the image of X when the
triangle is reflected across ̅̅̅̅. Which of the
following is an expression for the perimeter, in
inches, of quadrilateral X`YXZ ?
F. 2(y + z) + x
G. 2(x + y + z)
H. 2(x + y)
J. 2(x + z)
K. 2(y + z)
29. A pyramid composed of 4 congruent triangular
sides and a square base is shown “unfolded” in
the standard (x,y) coordinate plane below. Points
A, B, and C are vertices of 1 of the triangular
sides. What is the total surface area of the
pyramid?
26. A computer chip 0.32 cm thick is made up of
layers of silicon. If the top and bottom layers are
each 0.03 cm thick and the inner layers are each
0.02 cm thick, how many inner layers are there?
A. 13
B. 15
C. 16
D. 52
E. 64
Mr . Mosaad El Geneady
F. 240
G. 2√
H. 9
J. 20
K. 400
Mo: 01001851053
39
ACT
30.What is the area, in square inches, of the figure
below?
Geometry
33. The perimeter of a particular rectangle is 36 cm.
The longer sides of the rectangle are each 2 cm
longer than each of the shorter sides of the
rectangle . What is the length of one of the longer
sides of this rectangle ?
A. 8
B. 9
C. 10
D. 18
E. 32
A. 4
B
B. 6
C. 8
D. 9
10
A
E. 11
3
5
31. Rhombus RHOM e is shown below, If HR = 5m,
HM = 6m, then what is length of ̅̅̅̅
A. 3
B. 4
C. 5
D. 6
E. 8
32. In the figure is shown below, A right square
pyramid with equilateral triangular faces . The
slant height of the pyramid is 3√ inches. What
is the total length of all 8 edges of the pyramid?
34. What is the length of diagonal of the rectangular
solid shown in the figure above?
A.
B.
C.
D.
E.
11.18
11.58
14.18
15.44
20.18
35. If the volume of a cone is 24 cubic feet and its
height is 2 feet, what is the diameter of the base
A. 3
B. 6
C. 12
D. 24
E. 36
36. The right circular cylinder in the figure above
has height 3 inches and volume 48 cubic inches,
and segment AC is a diameter of the base. What
is the area, in square inches, of triangle ABC ?
F.
G.
H.
J.
K.
12
21
24
36
48•
Mr . Mosaad El Geneady
A. 6
B. 8
C. 12
D. 16
E. 24
Mo: 01001851053
ACT
Section (8)
1. A chord 24 inches long is 5 inches from the
center of a circle, as shown below. What is the
radius, to nearest tenth of an inch?
40
Geometry
4. Points A through F lie on the circle shown below
so that the distance between any 2 adjacent points
is equal. The circle has a diameter inches. What
is the length of ̅̅̅̅?
A.
B.
C. 3
D.
√
E.
A. 29.0
B. 24.5
C. 16.9
D. 13.0
E. 10.9
2. Points A and B lie on the circle below, where
Central angle ACB measure 110. What is
the measure ABC?
F. 35
G. 40
H. 45
J. 55
K. Cannot be determined from the given information
3. In the figure below, ̅̅̅̅ and ̅̅̅̅ are tangent to the
circle at B and C, and O is the center of the circle
If the measure of BAC is 40, What is the
measure of AOB ?
5. In the circle below, O is the center. Chord ̅̅̅̅ is
12 inches long and 8 inches from O. What is the
Area of the circle?
F. 36π
G. 64π
H. 80π
J. 100π
K. 208π
6. A circle with center C is shown below. Points
W, Z, Y, and Z lie on the circle. The measure of
WCY is 100, the measure of XCZ is 80,
the measure of WCZ is 150, What is the
measure of XCY?
A. 20°
B. 25°
C. 30°
D. 40°
E. 50°
7. The circumference of a circle is 50 cm. What
Is its diameter ?
F. 40
G. 50
H. 60
J. 70
K. 80
Mr . Mosaad El Geneady
F.
G.
H. 50
J. 25
K. 50
Mo: 01001851053
ACT
8. In the shown below, ̅̅̅̅ is 15 inches long, chord
̅̅̅̅ is 10 inches long, and ̅̅̅̅ is perpendicular to
̅̅̅̅ at D. How many inches long is ̅̅̅̅?
41
Geometry
12. A right circular cylinder is shown in the figure
below, with dimensions given in centimeters.
What is the total surface area of this cylinder, in
square centimeters?
(Note: The total surface area of a cylinder is given by
2r2 + 2rh where r is the radius and h is the
height.)
A. 10
B. 15
C. 5√
D. 5√
E. 10√
9. A circle with center C is shown below. Points
W, Z, Y, and Z lie on the circle. The measure of
WCY is 100, the measure of XCZ is 80,
the measure of WCZ is 150, What is the
measure of XCY?
A. 20°
B. 25°
C. 30°
D. 40°
E. 50°
10. The circumference of a circle is 50 cm. What
Is its diameter ?
F.
G.
H. 50
J. 25
K. 50
11. If the measure of one angle of a rhombus is
120and its perimeter is 16 cm, then what is the
length of its longer diagonal?
A. 4
B. √
C. √
D. √
E. √
Mr . Mosaad El Geneady
A. 300
B. 400
C. 500
D. 600
E. 1,600
13. The track for a model railroad display is set up
2 circles that are tangent to one another and
have diameters of 30 feet and 50 feet
respectively as shown below. The engine of
the train travels at a constant rate of 75 feet per
minute. To the nearest minutes, how many
minutes does the engine take to go in a figure
8 pattern around the entire exactly 1 time?
F.
G.
H.
J.
K.
1
2
3
4
7
14. What is the length of the edge of a cube having
the same total surface area as a rectangular prism
measuring 3 cm by 4 cm by 8 cm?
A. 22.7 cm
B. 4.8 cm
C. 136 cm
D. 5.8 cm
E. 11.7 cm
Mo: 01001851053
42
ACT
15. The circle below has a diameter of 8 cm. Which
of the following is closest to the area of the
square inscribed in the circle?
Geometry
16. Pablo has a deck and pool in his backyard. The
Deck`s shape is a rectangle with a semicircle
removed and is shown shaded in the figure below
The lengths of the straight sides of the deck are
given in feet. Pablo plans to cover the top of the
deck with stain. To decide how much stain to
purchase, he needs to find the area of the top of
the deck. To the nearest square foot, what is the
area of the top the deck?
A. 25
B. 32
C. 50
D. 64
E. 201
16. A can of soda pop has the shape of a right
circular cylinder with an inside height of 6 inches
and an inside diameter of 2 inches. When you
pour the soda pop from the full can into a
cylindrical glass with an inside diameter of
3 inches, about how many inches high is the soda
Pop in the glass?
( Note: The volume of right circular cylinder is r2h)
F.
G.
H.
J.
K.
2
4
5
6
8
F.
G.
H.
J.
K.
110
226
238
332
414
17. In the figure below points E, F,G, and H are on
The sides of square ABCD. arc ̂ has center at A
̂ at B, ̂ at C, and ̂ at D. All of the arcs
have a radius of 3 feet. What is the area of the
shaded region?
41. What is the volume of a sphere whose surface
area is 100π cm2?
A.
cm3
B.
cm3
C. 160π cm3
D.
cm3
E. 520 cm3
Mr . Mosaad El Geneady
A.
B.
C.
D.
E.
Mo: 01001851053
ACT
18. Secant AC and CE intersect at C, The chord AB
and DE are congruent , Minor arc ̂ measure
106. Minor arc ̂ measure 64. What is the
measure of arc ̂
43
Geometry
21. 2 circular pulleys with centers 8 inches apart are
connected with a tight belt. The belt warps of
the way around the large pulley, which has radius
of 5 inches, and of the way around the small
pulley, which has radius of 1 inch. What is the
exact length of the belt, in inches?
F. 42
G. 84
H. 85
J. 90
K. 95
19 . Graphed in the standard(x,y) coordinate plane
below is line l and the circle with equation
(x – 2 )2 + y2 = 1. Line l passes through O(0, 0)
and is tangent to the circle at A, and B is the
center of the circle. What is the measure of
AOB?
F. 15
G. 22.5
H. 30
J. 45
K. 60
20. A circle, 2 chords, are shown in the figure is
shown below, what is the value of x ?
F.
G.
H.
J.
K.
√
√
√
22. A small circle and a large circle are tangent at T,
as shown below. The center of the large circle
lies on the small circle. The diameter of the large
circle is 12 cm. What is the ratio of the area of the
small circle to the area of the large circle?
A.
B.
C.
D.
E.
A. 10
B. 13.5
C. 14
D. 17.5
E. 19
Mr . Mosaad El Geneady
Mo: 01001851053
ACT
23. The circle shown below had diameter ̅̅̅̅, and
points B and C lie on the circle. The measure of
CAD is 30, and the measure of minor arc ̂ is
60. What is the measure of minor arc ̂ ?
44
Geometry
26. The figure shown below is composed of a
rectangle and a semicircle. Points A and B are
endpoints of both a side of the rectangle and
a diameter of the semicircle. What is the
perimeter, in feet, of the figure?
F. 72
G. 98
H. 100
J. 108
K. 116
24. In the circle shown below, chords
and
intersect at P, which is the center of the circle,
and the measure ofPST is 30°. What is the
degree measure of minor arc ̂ ?
F. 30°
G. 45°
H. 60°
J. 90°
K. Cannot be determined from the given information
25. In the circle shown below, M is the center and
lies on ̅̅̅̅ and ̅̅̅̅ . Which of the following
statements is NOT true?
F. TUM measures 65°
G. ̅̅̅̅ .is parallel to ̅̅̅̅
H. ̂ measures 50°
J. ̅̅̅̅̅ ̅̅̅̅̅
K. ̅̅̅̅ ̅̅̅̅
Mr . Mosaad El Geneady
F. 3 + 20
G. 3 + 22
H. 6 + 14
J. 6 + 24
K. 9 + 48
27. The figure below consists of a square and
2 semicircles, with dimensions as shown.
What is the outside perimeter, in centimeters,
of the figure?
A. 8 + 8π
B. 16 + 8π
C. 16 + 16π
D. 32 + 8π
E. 32 + 16π
28. The diameter of one circle is 12 inches long. The
diameter of a second circle is 25%longer than the
diameter of the first circle. To the nearest square
inch, how much larger is the area of the second
circle than the area of the first circle?
F. 7
G. 28
H. 44
J. 64
K. 254
Mo: 01001851053
ACT
29. An 8-foot-square sheet of tin from which
4 identical circles are cut is shown below. Each
circle is tangent to 2 other circles and tangent to
2 of the edges of the square. What is the
approximate area of the remaining tin as
indicated by shaded region below?
A. 51.4
B. 38.9
C. 19.4
D. 13.7
E. 6.9
45
Geometry
32. A chord 24 inches long is 5 inches from the
center of a circle. What is the radius of the
the circle to nearest tenth of an inch?
A. 29.0
B. 24.5
C. 16.9
D. 13.0
E. 10.9
33. In the figure below, 2 tangent circles such that
the 10-centimeter diameter of the smaller circle
is equal to the radius of the larger circle. What
is the area of the shaded part?
30. Two concentric circles are shown below. The
radius of the larger circle is 10 feet and the radius
of the smaller circle is 6 feet. What is the area of
the shaded region bounded by the circles?
F. 8
G. 16
H. 36
J. 64
K. 100
31. The diagonal of a square is 12. What is the length
of a side?
A.
√
B. 14.1
C. 8.5
D. 6.9
E. 17
Mr . Mosaad El Geneady
F. 10
G. 75
H. 5π
J. 10π
K. 75π
34. A 6-inch-by-8-inch rectangle is inscribed in a
circle as shown below. what is the area of the
circle, in square inches?
F. 5π
G. 16π
H. 25π
J. 48π
K. 96π
Mo: 01001851053
46
ACT
35. In the figure below, AB BC, and ̅̅̅̅ is a
diameter of the circle, having a length of 4 cm.
what is the area of ABC ?
Geometry
38. The circumference of a circle is 20 cm. What is
length of the radius of the circle?
A.
B.
F.
G.
H.
J.
K.
2
4
8
√
4√
C.
D. 20
E. 20
36. As shown in the figure below, D is the center of
the circle, and right triangle ABD intersect the
circle at C and F. Point C is the midpoint of ̅̅̅̅,
12 cm long. The shaded region inside the circle
and outside the triangle has an area 32.
What is the measure of A?
F. 40
G. 45
H. 50•
J. 58•
K. 67.5•
37. The large with radius R inches is shown below;
3 small nonoverlapping circles, each with radius
r inches, are removed from the large circle.
remaining after the 3 circles were removed. What
is the area of the shaded region?
A. r2
B. R2
C. R2 – r2
D. R2 – 2r2
E. R2 – 3r2
Mr . Mosaad El Geneady
39. In the figure above, points A, B, C and D lie on
the circle. If the measure of arc ̂ is 160°,
what is the value of x ?
A.
B.
C.
D.
E.
16
20
32
40
64
40. What is the circumference of a circle whose
area is 64π cm2?
A. 16
B. 8π
C. 8
D. 128π
E. 16π
41. The circumference of a circle is 12 inches.
What is the area of the circle?
A. 4
B. 9
C. 12
D. 16
E. 36
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