1.
The figure below was formed by joining 2 segments of equal length at common endpoint Y.
If points X, Y, and Z are non-collinear, which of the following statements regarding XZ must always be true? a.
XZ = XY b.
XZ = 2(XY) c.
XZ > 2(XY) d.
XZ < 2(XY)
2.
A geometry student concluded:
If two sides and a non-included angle of one triangle are congruent to two sides and a non-included angle of another triangle, then the two triangles are congruent.
Which diagram can be used as a counterexample to the student’s conclusion?

3.
Which set of statements represents a valid deductive argument? a.
All quadrilaterals have 4 angles.
All parallelograms have 4 angles.
All quadrilaterals are parallelograms. b.
All parallelograms have diagonals that bisect each other.
All parallelograms have opposite sides that are parallel.
All polygons whose diagonals bisect each other have opposite sides that are parallel. c.
All rectangles have 4 right angles.
All squares have 4 right angles.
All rectangles are squares. d.
All parallelograms have 4 sides.
All polygons with 4 sides are quadrilaterals.
All parallelograms are quadrilaterals.
4.
In each of the circles below, four angles are formed by the intersection of 2 secant lines. The measures of two intercepted arcs and one angle are shown for the first three circles.
Which expressions can be used to represent m<ABC in degrees?
A.
B.
1
[(5𝑥 + 2) − (4𝑥 + 4)]
2
1
[(5𝑥 + 2) + (4𝑥 + 4)]
2
C.
2[(2𝑥 + 2) − (4𝑥 + 4)]
D.
2[(5𝑥 + 2) + (4𝑥 + 4)]

5.
Jake took pictures of Ana’s flag while she was practicing her routine for the football game, as shown below.
B.
Rotation, translation, translation
C.
Rotation, translation, dilation
D.
Reflection, translation, translation
6.
When viewed from above, the base of a water fountain has the shape of a hexagon composed of a square and
2 congruent isosceles right triangles as represented in the diagram below.
Which of the following best describes the movement of the flag from picture to picture?
A.
Reflection, rotation, translation
Which of the following measurements best represents the perimeter of the water fountain’s base in feet?
A.
(20 + 20√2)𝑓𝑡
B. (20 + 40√2)𝑓𝑡
C. (40 + 20√2)𝑓𝑡
D. (40 + 40√2)𝑓𝑡

7.
A side view of the intersection of a plane and a square pyramid is modeled below.
Which of the following best represents the shape formed by this intersection?
Which of the following best represents the shape formed by this intersection?
8.
The three-dimensional figure shown is composed of 11 identical cubes.
Which of the following could not represent a top, front, or side view of the figure?
Which of the following could not represent a top, front, or side view of the figure?

9.
Segment RG is graphed on the coordinate grid below.
Which of the following equations best represents the perpendicular bisector of segment RG?
A.
𝑦 =
1
3 𝑥 − 2
B.
𝑦 = −3𝑥 + 8
C.
𝑦 = 3𝑥 − 10
D.
𝑦 = −
1
3 𝑥 + 1
10.
Half of an international basketball court is shown below. The shaded region is composed of an isosceles trapezoid and a semicircle. The diameter of the semicircle is 3.6 meters.
If 1 meter is approximately equal to 3.28 feet, which of the following is closet to the area of the shaded region in square feet?
A.
32.9 ft 2
B.
409 ft 2
C.
354 ft 2
D.
108 ft 2
11.
In quadrilateral ABCD, conclusion?
A.
B.
Quadrilateral ABCD is a rectangle.
C.
Quadrilateral ABCD is an isosceles trapezoid.
D.
Which of the following statements is a reasonable

12.
Triangles RST and VSU are shown below.
13.
Triangle RST was dilated to create triangle R’S’T’, as shown on the coordinate grid below.
Which statement appears to be true?
A.
The center of dilation used to create ∆R’S’T’ was (-10,8).
B.
∆RST and ∆R’S’T’ are congruent.
C.
The scale factor used to create ∆R’S’T’ is 2.5.
D.
∆RST was reduced in size to create ∆R’S’T’.

14.
A tree’s shadow is 4.8 m long on level ground, as shown in the diagram.
The angle of elevation from the tip of the shadow to the sun is 50 degrees. Based on this information, which of the following is closest to the height of the tree?
A.
3.6 m
B.
5.7 m
C.
3.1 m
D.
7.5 m
15.
A company packages their product in two sizes of cylinders. Each dimension of the larger cylinder is twice the size of the corresponding dimension of the smaller cylinder.
Based on this information, which of the following statements is true?
A.
The volume of the larger cylinder is 2 times the volume of the smaller cylinder.
B.
The volume of the larger cylinder is 4 times the volume of the smaller cylinder.
C.
The volume of the larger cylinder is 8 times the volume of the smaller cylinder.
D.
The volume of the larger cylinder is 6 times the volume of the smaller cylinder.

16.
If ∆ ABC is similar to ∆ ADE, then AB: AD = ? : AE. Which replaces the “?” to make the statement true?
A. AC
B. AE
C. DE
D. BC
17.
A bisector of 𝑨𝑩 contains which line segment?
A 𝐶𝐺
B 𝐷𝐹
C 𝐷𝐺
D 𝐸𝐹

18.
Lines m and r are cut by a transversal.
What value of x will show that line m is parallel to line r ?
F 20
G 24
H 25
J 33
19.
If lines a and b are parallel, what is the value of x ?
A 120
B 115
C 65
D 60

20.
Which point lies on the bisector of angle PQR ?
F W
G X
H Y
J Z
21.
For what measure of ∠𝑫 is 𝑨𝑩
̅̅̅̅
in this figure?
A 26°
B 59°
C 69°
D 95°

22.
In the figure shown, line q is a transversal of parallel lines l, m, n, and p.
What are the values of x and y?
A x = 30, y = 30
B x = 30, y = 150
C x =150, y = 30
D x =150, y = 150
23.
In the figure shown, parallel lines j and k are cut by transversal m.
What is 𝒎∠𝟏 ?
F 32°
G 58°
H 122°
J 148°

24.
Lines y and z are cut by a transversal.
For what value of x is ∥ 𝒛 ?
A 13
B 77
C 103
D 154
25.
In this figure, 𝒎∠𝟏 = (𝟏𝟓𝒙 − 𝟓)° and 𝒎∠𝟐 = (𝟏𝟎𝒙 + 𝟑𝟓)° .
What is 𝒎∠𝟏 ?
F 31°
G 65°
H 85°
J 115°

26.
This figure represents line segments painted on a parking lot to create parking spaces.
Which equation can be used to show that these line segments are parallel?
A 118 −w = x
B 118 − x = w
C x +118 =180
D w +118 =180
For problems 27 – 29, underline the hypothesis and circle the conclusion of each statement.
State whether the conditional statement if true or false. If false, give a counterexample.
27.
If tomorrow is Friday, then today is Thursday.
28.
If a figure is a right triangle, then it has an angle with 90 degrees.
29.
If I am wearing red, then it is valentine’s day.
30.
Rewrite the following statement in if-then form.
All right triangles have an angle with a measure of 90 degrees.
[A] A figure has an angle with a measure of 90 degrees if and only if it is a right triangle.
[B] If a figure has an angle with a measure of 90 degrees, then it is a right triangle.
[C] A figure is a right triangle if and only if it has an angle with a measure of 90 degrees.
[D] If a figure is a right triangle, then it has an angle with a measure of 90 degrees.
31.
If I am invited, then I will go. What is the underlined portion in this conditional statement called?
32.
If I get the chance, then I will succeed. What is the underlined portion in this conditional statement called?
Find the complementary and supplementary angles for each.
33.
36⁰ _______ _______
34.
49⁰ _______ _______
35.
16⁰ _______ _______
36.
86⁰ _______ _______

37.
______________ Points that lie on the same line.
38.
______________ two angles whose sum is 180 degrees
39.
______________ an example that proves that a conjecture is false
40.
______________ is an argument that uses logic, definitions, properties and previously proven statements to show that a conclusion is true.
41.
______________ three side polygon
42.
______________ a statement that you believe to be true based on inductive reasoning
43.
______________ is a statement that can be written in the form of “p if and only if q”.
Means if p then q.
44.
______________ Points that lie on the same plane.
45.
______________ closed plane figure formed by three or more segments
46.
______________ four sided polygon
47.
______________ two angles whose sum is 90 degrees
48.
______________ the process of reasoning that a rule or statement is true because specific cases are true.
49.
Which expression can be used to find the values of c(n) in the table below?
a.
C( n ) = n + 5 b.
C( n ) = 6 n c.
C( n ) = 4 n + 2 d.
C( n ) = 4 n - 2

50.
Simplify the algebraic expression
2 ( x

5 )( x

2 )

( x
2 
10 x

18 ) a.
3𝑥 2 -16x-2 b.
𝑥 2 − 4𝑥 − 2 c.
𝑥 2 +13x+8 d.
𝑥 2 -7x+8
51.
What is the domain of this function?
a.
0 ≤ 𝑥 ≤ 16 b.
−8 ≤ 𝑥 ≤ 0 c.
0 ≤ 𝑦 ≤ 16 d.
−8 ≤ 𝑦 ≤ 0
52.
What is the dependent variable in the table below? a.
1 b.
7 c.
N d.
C(n)

53.
The number of neon fish doubles every month in a fish aquarium. If Joe put 8 neons in his his tank after 3 months? a.
8 b.
24 c.
48 d.
64
54.
Which equation best represents the area of the rectangle below? a.
2x +12 b.
x 2 - 3x c.
x 2 - 6x d.
4x – 6 x x – 3
55.
Which expression is equivalent to 1
2 a.
6x – 5y
(12𝑥 − 8𝑦) + 2(𝑥 + 3𝑦) ? b.
8x + 2y c.
13x – 5y d.
8x – 10y
56.
Solve this equation: 2x – 3 – x = 15 – 5x
57.
Which equation best represents the perimeter of the rectangle below? a.
2x + 12 b.
x 2 - 3x x c.
x 2 – 6x d.
4x – 6 x – 3
58.
The sales tax rate is 8.75%. Which equation shows the total cost, c, of an item including sales tax, when x represents the price of the item before tax is added? a.
C = 0.0875x b.
C = 1.0875x c.
C = x + 0.0875 d.
C = 0.875x

59.
∆𝑻𝑹𝑮 is a right triangle.
Which is closest to the length of 𝑹𝑻 ?
A.
5
B.
11
C.
14
D.
28
60.
Which list has the sides of ∆𝑨𝑩𝑪 ordered from longest to shortest?
F. 𝐵𝐶 ̅̅̅̅, 𝐴𝐵
G. 𝐴𝐵
H. 𝐴𝐶
J. 𝐵𝐶 ̅̅̅̅, 𝐴𝐶
61.
Three survey markers are located on a map at points H, I, and J. A triangle is formed by connecting these markers by string so that 𝑯𝑰 = 𝟏𝟓𝟎 𝐟𝐞𝐞𝐭 , 𝑯𝑱 = 𝟐𝟒𝟓 𝐟𝐞𝐞𝐭 , and 𝑰𝑱 = 𝟑𝟔𝟓 𝐟𝐞𝐞𝐭 .
Which statement is true about the measures of the angles of ∆𝑯𝑰𝑱 .

A.
𝑚∠𝐻 is the smallest
B.
𝑚∠𝐻 is the largest
C.
𝑚∠𝐼 is the smallest
D.
𝑚∠𝐼 is the largest
62.
In the figure, what is the value of 𝒙 ?
F. 6
G.
6√2
H. 6√3
J. 12
63.
Two sides of a triangle measure 14 inches and 8 inches. Which cannot be the length of the remaining side?
A.
6 in.
B.
8 in.
C.
14 in.
D.
21 in.
64.
In the circle, what is the measure of ∠𝑨𝑩𝑪 ?

F. 30°
G.
60°
H.
120°
J. 140°
65.
This figure shows a pattern of triangles and regular hexagons.
What is the value of 𝒙 ?
A.
30
B.
60
C.
90
D.
120
66.
Which figure has all sides of equal measure but not necessarily all angles of equal measure?
F. Square
G. Rectangle
H. Rhombus
J. Trapezoid

67.
What is 𝒎∠𝑫𝑨𝑹 in circle A?
A.
17°
B.
34°
C.
56°
D.
68°
68.
Two chords intersect with the measures shown in the drawing.
What is the value of 𝒙 ?
F. 8.0
G. 9.5
H. 10.0
J. 14.5
69.
In rectangle 𝑨𝑩𝑪𝑫 , the slope of 𝑨𝑩 is
1
2
. What is the slope of 𝑪𝑫 ?
A. −2
B. −
C.
1
2
1
2
D. 2
70.
In the figure shown, what is 𝒎∠𝑾𝑿𝒀 ?

F. 45°
G. 107°
H. 120°
J. 135°
71.
𝑫𝑬𝑭𝑮 is a rhombus with 𝒎∠𝑬𝑭𝑮 = 𝟐𝟖° .
What is 𝒎∠𝑮𝑫𝑬 ?
A.
14°
B.
28°
C.
30°
D.
56°
72.
This figure is a traffic sign in the shape of a regular octagon.
What is the value of 𝒙 ?

F. 45
G. 60
H. 135
J. 180
73.
A rectangular rug is 24 feet long and 10 feet wide. A rhombus design is formed inside the rug by joining the midpoints of each side of the rectangle. What is the length of each side of the rhombus?
A.
13 ft
B.
26 ft
C.
169 ft
D.
240 ft
74.
A man who is 6 feet tall casts a shadow that is 4 feet long. At the same time, a nearby flagpole casts a shadow that is 18 feet long. How tall is the flagpole?
F. 10 ft
G. 12 ft
H. 22 ft
J. 27 ft
75.
A fish tank in the shape of a rectangular prism has these dimensions:

Length = 20 inches

Width = 10 inches

Height = 12 inches
What is the volume of water in the tank when it is
4
5
full?
A.
1,120 cu in.
B.
C.
D.
1,920 cu in.
2,400 cu in.
3,000 cu in.
76.
folded?
Which of these nets would form a cube when

77.
If a cube with side length 6 inches has its dimensions divided in half, what will be the volume of the new cube?
A.
108 cubic inches
B.
54 cubic inches
C.
27 cubic inches
D.
9 cubic inches
78.
A right cone is placed on its circular base.
Which statement about the cone is incorrect?
F. The view from the front is a triangle.
G. The view from the bottom is a circle.
H. The view from the top is a circle.
J. The view from the left is a rhombus.
79.
A cone has a slant height of 10 centimeters and a lateral area of 60𝜋 square centimeters. What is the volume of a sphere with a radius equal to that of the cone?
A.
102𝜋 𝑐𝑚
3
B.
144𝜋 𝑐𝑚 3
C.
288𝜋 𝑐𝑚
3
D.
1,333𝜋 𝑐𝑚 3
80.
Which line of reflection maps point 𝑲 at (−𝟐, 𝟐) to point 𝑲
′
at (𝟐, −𝟐) ?
F. 𝑦 = 2
G. 𝑦 = 𝑥
H. 𝑥 − 𝑎𝑥𝑖𝑠
J. 𝑦 − 𝑎𝑥𝑖𝑠
81.
If the coordinates of A are (1, 1) and the midpoint of 𝐴𝐵 is (−2, 0) , then the coordinates of B are –
A.
(−0.5, 0.5)
B.
(0.5, 0.5)
C.
(−1, 0)
D.
(−5, −1)

82.
Which transformation could move the triangle 𝑷 to triangle 𝑷
′
in a single step?
F. Reflection over 𝑥 = 4
G. Rotation about (2, 3)
H. Reflection over 𝑦 = 4
J. Translation
83.
Figure STARFIND is symmetric with respect to the 𝑥 − 𝑎𝑥𝑖𝑠 . The coordinates of point A are (8, 6) . What are the coordinates of point N?
A.
(8, −6)
B.
(6, −8)
C.
(−6, 8)
D.
(−8, 6)

Answer Key for Geometry Problem Bank
1.
D
2.
D
3.
D
4.
B
5.
A
6.
D
7.
D
8.
C
9.
A
10.
C
11.
C
12.
B
13.
C
14.
B
15.
C
16.
A
17.
D
18.
F
19.
D
20.
H
21.
C
22.
B
23.
F
24.
B
25.
J
26.
D
27.
If tomorrow is Friday, then today is Thursday. True
28.
If a figure is a right triangle, then it has an angle with 90 degrees. True
29.
If I am wearing red, then it is valentine’s day. False, it could be Christmas or Red ribbon week
30.
D
31.
conclusion
32.
hypothesis
33.
54 ° , 144 °
34.
41 °, 131°
35.
74 °, 164°
36.
4 °, 94°
37.
collinear
38.
supplementary
39.
counterexample
40.
proof
41.
triangle

75.
B
76.
F
77.
C
78.
J
79.
C
80.
G
81.
D
82.
J
83.
A
64.
F
65.
A
66.
H
67.
D
68.
F
69.
C
70.
J
71.
B
72.
F
73.
A
74.
J
51.
B
52.
D
53.
D
54.
B
55.
B
56.
3
57.
D
58.
B
59.
C
60.
J
61.
B
62.
G
63.
A
42.
conjecture
43.
Bi-conditional statement
44.
coplanar
45.
polygon
46.
quadrilateral
47.
Complementary
48.
Inductive reasoning
49.
C
50.
B