Geometry Final Exam Review

2014 – 2015

- This review covers the major topics in the material that will be tested on the final exam.

It is not necessarily all inclusive and additional studying and problem solving practice

may be required to fully prepare for the final.

- Use additional paper, if necessary.

- Calculators may be used on this review packet as well as the final exam.

Directions:

Questions 1 – 50: True-False and Multiple Choice. Circle the correct

answer or put it in the space provided.

Questions 51 – 75: Matching. Place the letter of your answer in the space

provided.

Questions 76 – 100: Free Response. Simplify all answers. Place your final

answer for each question in the space provided and show

all work if you want to receive credit!! If no work is

shown, the question will automatically be marked wrong.

This review is due FOR A GRADE on or before _________________________.

Name __________________________________

Teacher ________________________________

Period_______________________

Part 1 – Determine whether each statement is true (T) or false (F). T F 1. Some circles have a radius of 1. T F 2. If the scale factor of one triangle to another is 1:4, then the ratios of the areas is 1:16. T F 3. If the measure of one acute angle of a right triangle is 30°, then the measure of the other

acute angle is 60°. T F 4. If the legs of a right triangle are congruent, each acute angle has a measure of 45°. T F 5. If two similar solids have a scale factor of 2:3, then the ratio of their volumes is 4:9. T F 6. A dodecagon has twenty sides. T F 7. When a central angle and an inscribed angle intercept the same arc, the two angles are

congruent. T F 8. A tangent to a circle is perpendicular to the radius drawn to the point of tangency. T F 9. The measure of each interior angle of a regular hexagon is 120°. T F 10. An angle inscribed in a semicircle is a right angle. T F 11. If two circles are congruent, then their diameters are congruent. T F 12. If a diameter is perpendicular to a chord, then it bisects the chord. T F 13. A circle with an area of 121 units2 has a circumference of 11 units.

T F 14. All angles which intercept congruent arcs of a circle are congruent. T F 15. The central angle of a regular decagon is 36°. T F 16. The sine ratio is defined to be the ratio of the length of the adjacent leg to the length of

the hypotenuse. T F 17. The area of a right triangle with side lengths of 3, 4, and 5 is 6 units. T F 18. Opposite angles of an inscribed quadrilateral are complementary.

Part 2 – Determine if each statement is ALWAYS (A), SOMETIMES (S), or NEVER (N) true. 19. A radius of a circle is ___________ a chord of the circle. 20. The diagonals of a quadrilateral are ___________ perpendicular. 21. The bases of a trapezoid are ___________ parallel. 22. A trapezoid is ___________ a parallelogram. 23. The exterior angles in a triangle _____________ add up to 360°.

Part 3 – Multiple Choice. Choose the BEST answer and place it in the space provided. ______ 24. Which of the following is not an isometry? a. translation b. rotation c. reflection d. dilation

For 25 and 26, use the diagram to the right. ______ 25. If AC = 8 and AB = 17, find CB. a. 18.8 b. 15

c. 225 d. 9 ______ 26. If m A 56 , find m BCD.

a. 44° b. 34°

c. 90° d. 56° ______ 27. Find the perimeter of a square whose area is 36. a. 6 b. 12 c. 24 d. 36

______ 28. For MNO, the length of NO is

a. 5 2 b. 10

c. 5 3 d. 10 3

______ 29. If the perimeter of a square equals 20, then the area of the square is a. 5 b. 10 c. 25 d. 50

D

C

B A

30

10

ON

M

______ 30. If the sides of a triangle are 3, 4, and 6, then the triangle is a. an obtuse triangle b. an isosceles triangle c. an acute triangle d. a right triangle ______ 31. Which set of sides represent a right triangle? a. 1, 2, 3 b. 2, 3, 4 c. 3, 4 , 5 d. 4, 5, 6

For 32 and 33, use the diagram to the right. ______ 32. In RST, if m S 90 , then tan R =

a. TS

RS b.

RS

TS c.

TS

RT d.

RS

RT

______ 33. In RST, if m S 90 , then sin T =

a. TS

RT b.

RS

TS c.

RS

RT d.

RT

RS

______ 34. Two rectangles have a scale factor of 2:5. If the area of the smaller rectangle is 128 units2, find the area of the larger rectangle. a. 320 units2 b. 800 units2 c. 25 units2 d. 750 units2 ______ 35. What is the reflection image of V over line b? a. X b. W c. Y d. T

For 36 and 37, use circle R to the right. ______ 36. A major arc of circle R is

a. DEF b. EF c. DGF d. ED

______ 37. In circle R, mGD mDF

a. mDEF b. mGDE c. mGFD d. mGDF

TS

R

b Y

X WV

T

U

G

F

E

D

R

For 38 – 40, use circle O to the right. ______ 38. The measure of ABC

a. 100° b. 90° c. 80° d. 70° ______ 39. The measure of A a. 40° b. 50° c. 60° d. 70° ______ 40. The measure of AXD a. 85° b. 95° c. 55° d. 100° ______ 41. Quadrilateral WXYZ is inscribed in circle P. If m X 80 and

mXW 105 , then mXY

a. 95° b. 100° c. 105° d. 110° ______ 42. Find the area of a circle whose circumference is 10 .

a. 5 b. 20 c. 25 d. 100

For 43 and 44, use circle S to the right.

______ 43. If mFG 80 and mEC 44 , then m D

a. 62° b. 38° c. 22° d. 18° ______ 44. If CX = 12, XG = 2, and XH = 3, then XF = a. 12 b. 8 c. 4.5 d. 2 ______ 45. The length of a diagonal of a square is 6. The length of each side is

a. 6 2 b. 3 2 c. 6 d. 3

P

Z

Y

XW

100

110

X

OD

CB

A

S

F

XG

HC

E

D

______ 46. The transformation given is an isometry. What are the value of the variables? a. x = 41, y = 6, z = 6 b. x = 40, y = 6, z = 9 c. X = 6, y = 40, z = 6 d. x = 41, y = 40, z = 6 ______ 47. How many lines of symmetry does the polygon to the right appear to have? a. 0 b. 1 c. 2 d. 5 ______ 48. The measure of a central angle in a regular pentagon is a. 5° b. 72° c. 108° d. 540° ______ 49. A standard equation of a circle with center (–4, 3) and radius 7 is a. (x + 4)2 + (y – 3)2 = 49 b. (x – 4)2 + (y + 3)2 = 7 c. (x + 4)4 + (y – 3)2 = 7 d. (x – 4)2 + (y + 3)2 = 49 ______ 50. A right cylindrical container has a radius of 12 centimeters and a height of 15 centimeters. A right conical container’s base has a diameter of 24 centimeters. If the conical container has the same volume as the cylindrical container, what is the height of the conical container? a. 11.25 cm b. 7.5 cm c. 15 cm d. 45 cm

(2x + 19)

3z

42

(8y - 6)

18

101

ML

K

J

D C

B

A

Part 4 – Matching.

SET 1 – Match each solid with its corresponding name. _____ 51. _____ 52. A. Regular pyramid B. Triangular prism C. Cone D. Cylinder _____ 53. _____ 54. E. Rectangular prism _____ 55.

SET 2 – Match each diagram with its arc length or area of the sector. _____ 56. area of smaller sector _____ 57. area of smaller sector A. 4.7 B. 26.2 C. 9.8 D. 4.2

_____ 58. length of AB _____ 59. area of larger sector E. 111.2

_____ 60. length of AB

SET 3 – Match each part of the circle to its correct name. Be specific!

_____ 61. CG A. chord

_____ 62. DE B. secant _____ 63. D C. diameter

_____ 64. AB D. point of tangency

_____ 65. HF E. tangent _____ 66. ODE AB. inscribed angle

_____ 67. 1 AC. central angle _____ 68. 2 AD. radius

_____ 69. OD AE. right angle

2

1

O

H

G

F

E

D

C

B

A

SET 4 – Find each value using the possibilities given.

_____ 70. Find x. A. 12 3

B. 49

_____ 71. Find y. C. 6 2

D. 6 3

_____ 72. Find a. E. 6 F. 26.2 _____ 73. Find b. _____ 74. Find e. _____ 75. Find f.

yx

6

30

18

ba

f

e

41

40

Part 5 – Free Response. Solve for the indicated values. Show all work. Round answers to

the nearest tenth, when appropriate, and place answers in the space provided. 76. Find x and y.

x = __________

y = __________ 77. A quadrilateral has the vertices A(0, 3), B(6, 6), C(0, 6), and D(–3, 3). Graph the image after a

dilation with a scale factor of 1

.3

78. Graph the given circle: (x – 1)2 + (y + 3)2 = 4 79. Find the area of this right triangle if b = 15 and c = 17.

A = __________ 80. A triangle has side lengths of 6, 9, and 11. Decide whether it is an acute, right, or obtuse triangle. Explain.

Classification = __________ Explanation – ______________________________________

y

x

124

65108

c

b

a

81. Find the values of x and y.

x = __________

y = __________ 82. Find the value of x.

x = __________

83. Find mPQ in circle A. Drawing is not necessarily to scale.

mPQ = __________

84. What must be the measures of B and C so that a circle can be circumscribed about ABCD?

Diagram is not drawn to scale.

m B = __________

m C = __________

85. Find the value of x if mAB 76 and mCD 35 .

x = __________

F E

D

x

4

53

78103

D

C

B

A

x

O

D

C

B

A

(2y - 15)

(y + 35)S R

QP

A

14y

x

36

86. Find the sum of the measures of the interior angles of a decagon.

sum = __________ 87. Find the number of sides of a regular polygon with each interior angle equal to 150°.

number of sides = __________ 88. Find the measure of an interior and an exterior angle of a regular polygon with 15 sides.

interior angle = __________

exterior angle = __________ 89. Find the volume of the cylinder.

volume = __________ 90. Find the surface area of the rectangular prism.

surface area = __________ 91. Find the lateral area of the cone.

lateral area = __________ 92. Find the volume of the pyramid.

volume = _______

8 in.

10 in.

6 in.

17 m

15 m

16 m

16 m

93. Find the surface area and the volume of the sphere.

surface area = __________

volume = __________ 94. An 8 foot ladder is leaning against a house and makes a 48° angle with the ground. How far is the foot of the ladder from the house?

distance = __________ 95. What is the scale factor of two spheres if their ratio of surface areas is 36:49?

scale factor = __________ 96. Solid A has a volume of 189 ft3 and solid B has a volume of 875 ft3. If solid B has a surface area of 320 ft2, find the surface area of solid A.

surface area of solid A = __________ 97. Identify the center and radius of the given circle: x2 + (y + 6)2 = 49

center = __________

radius = __________ 98. Write the equation of a circle whose center is (3, –3) and has a point on the circle at (3, –9). Suggestion – use graph paper!

equation: ______________________________ 99. When given a right triangle and two of the sides, what formula should you use to find the third side? 100. Are you going to pass the final?