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Geometry

Total questions: 60

Worksheet time: 30mins

Name
Class
Date
1.

QR is located at Q(-5, -8) and R(-1, 3). Which pair of points would form a segment congruent to QR?

a)

(7, 4) and (-3, 5)

b)

(-10, 2) and (-1, 6)

c)

(3, -5) and (1, -6)

d)

(-4, 9) and (7, 5)

2.

If SW ⟂ RT, m∠RSU = (5x + 17)°, and m∠VST = (9x – 11)°, find m∠WSV.

a)

34°

b)

38°

c)

52°

d)

66°

3.

Which diagram shows a pair of angle measures that prove j || k?

a)

(Diagram with j, k, l, m and angles 105°, 105°)

b)

(Diagram with j, k, l, m and angles 105°, 75°)

c)

(Diagram with j, k, l, m and angles 75°, 75°)

d)

(Diagram with j, k, l, m and angles 75°, 105°)

4.

What value of x would prove a || b?

a)

8

b)

9

c)

10

d)

11

5.

A crosswalk connects two sidewalks along the street below. If the sidewalks are parallel, what is the value of x?

a)

66°

b)

114°

c)

126°

d)

156°

6.

If BC || DE, find the value of x.

a)

3

b)

4

c)

5

d)

6

7.

The graph of line l is shown below. Which of the following represents the slope of a line parallel to line l?

a)

-3

b)

3

c)

-1/3

d)

1/3

8.

JK has coordinates J(-3, 9) and K(5, -1). If LM is perpendicular to JK, what is the slope of LM?

a)

4/5

b)

-4/5

c)

5/4

d)

-5/4

9.

Which equation represents a line parallel to y = -2x + 9?

a)

2x - 4y = 28

b)

2x + 4y = 28

c)

4x - 2y = 10

d)

4x + 2y = 10

10.

Which proves as a counterexample to the statement "All capital letters have at least one line of symmetry."

a)

S

b)

C

c)

Y

d)

H

11.

Let p represent "Vertical angles are congruent" and q represent "All apples are red." Which symbolic notation represents a true statement?

a)

p ∧ q

b)

~p ∨ q

c)

p ∧ ~q

d)

~p ∧ q

12.

Which is the converse of the statement?

a)

If a quadrilateral is not a square, then its diagonals are not perpendicular.

b)

If the diagonals of a quadrilateral are perpendicular, then it is a square.

c)

If the diagonals of a quadrilateral are not perpendicular, then it is not a square.

d)

If a quadrilateral is not a square, then its diagonals are perpendicular.

13.

Statement A: "If Lindsay is traveling on an airplane, then she will need a boarding pass." Statement B: "If Lindsay does not need a boarding pass, then she is not traveling on an airplane." Statement B is the –

a)

Inverse

b)

Converse

c)

Contrapositive

d)

Biconditional

14.

Which of the following statements is false?

a)

A. Two circles are congruent if and only if they have the same radius.

b)

B. The product of two numbers is even if and only if both numbers are even.

c)

C. Today is Monday if and only if yesterday was Sunday.

d)

D. Two lines are parallel if and only if they have the same slope.

15.

Following the statements below, which of the following represents a valid conclusion? Given: If the basketball player makes the shot, then the team will win the game. Given: If the team wins the game, then they will advance to the playoffs.

a)

If the basketball player does not make the shot, then the team will not win the game.

b)

If the basketball player does not make the shot, then the team will not advance to the playoffs.

c)

If the team does not win the game, then the team will not advance to the playoffs.

d)

If the basketball player makes the shot, then the team will advance to the playoffs.

16.

The Venn diagram below shows the relationship of first quarter awards given to students in Mrs. Hogan’s homeroom class. Which statement is false?

a)

A. All students who made honor roll also made merit roll.

b)

B. Some students who had perfect attendance also made honor roll.

c)

C. All students on merit roll also made honor roll.

d)

D. Some students are on merit roll, honor roll, and had perfect attendance.

17.

Two sides of a triangle measure 18 meters and 13 meters. Which of the following measures could represent the perimeter of the triangle?

a)

34 meters

b)

37 meters

c)

62 meters

d)

68 meters

18.

Park Street, Scott Street, and Oak Street form a triangle. If the angle formed by Oak Street and Park Street is 62° and the angle formed by Park Street and Scott Street is 58°, which lists the sides of the triangle from least to greatest?

a)

Park Street, Oak Street, Scott Street

b)

Scott Street, Park Street, Oak Street

c)

Scott Street, Oak Street, Park Street

d)

Oak Street, Park Street, Scott Street

19.

Which values of x and y make ΔCDE ≅ ΔHFG?

a)

x = 8, y = 6

b)

x = 8, y = 7

c)

x = 13, y = 6

d)

x = 13, y = 7

20.

What additional piece of information would prove ΔLMK ≅ ΔNMK by Side-Angle-Side?

a)

M is the midpoint of LN

b)

∠LMK ≅ ∠NMK

c)

∠MLK ≅ ∠NMK

d)

MK bisects ∠LKN

21.

Using the information given on the diagram, which congruence postulate or theorem can be used to prove ΔPSR ≅ ΔRQP?

a)

Side-Side-Side

b)

Side-Angle-Side

c)

Angle-Side-Angle

d)

Angle-Angle-Side

22.

A partial proof is given below. Use the information given to complete questions 22-25. Given: AB ≅ DE; C is the midpoint of BE Prove: ΔABC ≅ ΔDEC Which reason justifies statement 2?

a)

A. Vertical Angles

b)

B. Alternate Interior Angles

c)

C. Corresponding Angles

d)

D. Consecutive Interior Angles

23.

Which reason justifies statement 3?

a)

Reflexive Property

b)

Transitive Property

c)

Definition of Midpoint

d)

Definition of Congruent Sides

24.

Which reason justifies statement 4?

a)

Vertical Angles

b)

Alternate Interior Angles

c)

Corresponding Angles

d)

Consecutive Interior Angles

25.

Which reason justifies statement 5?

a)

Side-Side-Side

b)

Side-Angle-Side

c)

Angle-Side-Angle

d)

Angle-Angle-Side

26.

ΔMNP is shown on the graph below. If ΔQRS has coordinates Q(-6, -7) and R(-8, -1), what could be the coordinates of S if ΔMNP ≅ ΔQRS?

a)

(-2, -2)

b)

(-1, -5)

c)

(-3, 1)

d)

(0, -6)

27.

If ΔVWZ ~ ΔWXY, find the length of YX.

a)

14

b)

18

c)

20

d)

22

28.

If ∠K ≅ ∠P, which additional piece of information is sufficient to prove ΔJKL ~ ΔNPM by Side-Angle-Side Similarity?

a)

JK/NP = JL/NM

b)

KL/PM = JL/NM

c)

JK/NP = KL/PM

d)

JK/JL = NP/NM

29.

Based on the given information, which diagram contains a pair of similar triangles?

a)

(Diagram with sides 28, 36, 20, 16)

b)

(Diagram with angles 64°, 91°, 25°)

c)

(Diagram with two triangles)

d)

(Diagram with two triangles and arrows)

30.

Given the side measures, which of the following could form a right triangle?

a)

61 m, 60 m, 11 m

b)

24 in, 34 in, 28 in

c)

55 ft, 45 ft, 35 ft

d)

48 cm, 46 cm, 15 cm

31.

The diagram shows the locations of Cody and Reese after running different directions from a tree. How far did Cody run?

a)

50 yd

b)

64 yd

c)

75 yd

d)

80 yd

32.

If △ABC is an equilateral triangle and BD = 36 inches, find the value of x.

a)

12√3

b)

18√3

c)

24√3

d)

36√3

33.

If the perimeter of a square is 68 feet, find the approximate length of its diagonal.

a)

17 feet

b)

24 feet

c)

38 feet

d)

48 feet

34.

Which angle measure is closest to the value of x?

a)

39.8°

b)

50.1°

c)

56.4°

d)

33.6°

35.

An 85 foot wire is tied from the top of a utility pole to the top of the building. Find d, the distance from the pole to the building.

a)

75.2 ft

b)

78.8 ft

c)

80.5 ft

d)

82.1 ft

36.

Jayden is on his boat riding through the Cooper River. He spots the Cooper River Bridge at an angle of elevation of 42°. If the bridge stands 761 feet above Jayden’s viewing point on the boat, what is the horizontal distance from Jayden to the bridge?

a)

804.7 feet

b)

845.2 feet

c)

893.4 feet

d)

915.1 feet

37.

If the sum of the interior angle measures of a convex polygon is 2,160°, how many sides does the polygon have?

a)

12 sides

b)

13 sides

c)

14 sides

d)

15 sides

38.

If each interior angle of a regular hexagon measures (13x + 3)°, find the value of x.

a)

x = 9

b)

x = 10

c)

x = 11

d)

x = 12

39.

Rhombus JKLM is shown below. Find m∠KLM.

a)

A. 36°

b)

B. 38°

c)

C. 72°

d)

D. 76°

40.

If QRST is an isosceles trapezoid, find m∠LR.

a)

107°

b)

113°

c)

118°

d)

125°

41.

Which quadrilateral always has diagonals that are congruent but not necessarily perpendicular?

a)

Parallelogram

b)

Rectangle

c)

Rhombus

d)

Square

42.

Parallelogram CDEF has vertices C(-4, -4), D(-2, 0), E(6, 2) and F(4, -2). Which ordered pair represents the intersection of the diagonals?

a)

(-3, -2)

b)

(5, 0)

c)

(1, -1)

d)

(0, -3)

43.

Which transformation was used to map F'G'H'?

a)

Reflection over x = -1

b)

Reflection over y = -1

c)

Rotation 90° counterclockwise about the origin.

d)

Rotation 270° counterclockwise about the origin.

44.

Rhombus STUV is located at S(-5, 4), T(-1, 5), U(-2, 1), and V(-6, 0). If STUV is translated along the rule (x, y) → (x + 7, y - 8), which quadrant will the new rhombus be located?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

45.

Identify the scale factor that was used to graph ΔW'X'Y'.

a)

1/2

b)

1/3

c)

2/3

d)

3/2

46.

Which is not a line of symmetry in the figure below?

a)

x = -4

b)

y = 4

c)

y = x

d)

y = -x

47.

A regular pentagon has what type of symmetry?

a)

Line symmetry only

b)

Point symmetry only

c)

Both point and line symmetry

d)

Neither point nor line symmetry

48.

Given circle S, find m∠TUV.

a)

32°

b)

28°

c)

58°

d)

36°

49.

If ED is tangent to circle H, find the value of x.

a)

x = 6

b)

x = 7

c)

x = 8

d)

x = 9

50.

Chords AB and CD intersect as shown below. Find the length of CD.

a)

18

b)

39

c)

42

d)

51

51.

Given the circle below, find PQ.

a)

17

b)

21

c)

25

d)

28

52.

Four streets feed into a roundabout circle. If the diameter of the roundabout is 130 feet, find the approximate distance a car will travel between Cole Street and Maple Street along the roundabout.

a)

98.5 feet

b)

107.2 feet

c)

119.2 feet

d)

125.9 feet

53.

Which is closest to the area of the shaded sector of circle C?

a)

29 cm²

b)

34 cm²

c)

38 cm²

d)

45 cm²

54.

The points (0, -8) and (10, 2) represent the endpoints of a diameter of a circle. Which of the following represents the equation of this circle?

a)

(x + 5)² + (y - 3)² = √50

b)

(x - 5)² + (y + 3)² = √50

c)

(x + 5)² + (y - 3)² = 50

d)

(x - 5)² + (y + 3)² = 50

55.

A square base pyramid is shown below. Find its surface area.

a)

971.8 ft²

b)

1,094.4 ft²

c)

288π ft²

d)

2,304π ft²

56.

Mikayla is filling a glass sphere with water. If the diameter of the sphere is 12 inches, what is the minimum amount of water she needs to completely fill the sphere?

a)

576π in³

b)

144π in³

c)

288π in³

d)

2,304π in³

57.

The diameter of a cone is 16 meters. If the height is 1.5 times its radius, which value is closest to the volume of the cone?

a)

752.9 m³

b)

789.4 m³

c)

804.2 m³

d)

824.8 m³

58.

The cardboard box below is used by a company to package new laptops. If the company plans to increase the length of the box by 2 inches, what is the minimum amount of extra cardboard needed to construct the new box?

a)

84 in²

b)

116 in²

c)

132 in²

d)

160 in²

59.

The volume of Prism A is 1,536 m³ and the volume of Prism B is 375 m³. What is the ratio of their surface area?

a)

A. 8:5

b)

B. 64:25

c)

C. 16:25

d)

D. 512:125

60.

The radius of a cylinder is multiplied by 6 while the height is kept the same. What effect does this have on the volume of the cylinder?

a)

6

b)

12

c)

36

d)

216