# Geometry Honors Final Exam Review June 2018

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1 Geometry Honors Final Exam Review June Determine whether 128 feet, 136 feet, and 245 feet can be the lengths of the sides of a triangle. 2. Casey has a 13-inch television and a 52-inch television in her home. What is the ratio of the sizes of the smaller TV to the larger TV? 3. If EFG EJK, find x, JK, KG, and the scale factor relating EFG to EJK. 4. Find the value of y. 5. Find the perimeter of ABC if ABC XYZ. 6. Find the magnitude of PQ %%%%% if P( 5, 3) and Q(2, 1). 7. Find the geometric mean between 27 and 42. Round to the nearest tenth. 8. Determine whether 27, 120, and 123 are the measures of the sides of a right triangle. Then explain whether they form a Pythagorean triple. 9. The diagonal of a square is 56 centimeters long. Find the perimeter of the square to the nearest tenth. 10. Find m P to the nearest degree in right MNP for M(3, 6), N(3, 8), and P( 5, 8). For Questions 11 and 12, refer to the figure. Round to the nearest tenth. 11. Find m S if m T = 68, t = 65, and s = Solve RST if t = 17, s = 11, and m R = Construct the reflected image of the quadrilateral in line l. 1

2 14. Triangle QST with vertices at Q(9, 5), S(12, 8), and T(6, 3) is translated so that S is at (17, 9). Find the coordinates of Q and T. 15. Determine the order and magnitude of the rotational symmetry of a regular decagon. 16. The endpoints of XY ++++ are X( 2, 3) and Y(7, 4). The segment is translated along the vector 3, 1 and then reflected in the x-axis. What is the coordinate of X? 17. Determine the scale factor used for the dilation of the figure with center C. Then state whether the dilation is an enlargement, reduction, or congruence transformation. 18. Find the coordinates of the image of B(3, 5) along the translation 6, A band of sequins that measures 108 inches is cut into two pieces so that their lengths are in a 5:7 ratio. Find the length of each piece. 20. A square ABCD centered at the origin is dilated with a scale factor of Next, the image A B C D is dilated by a scale factor of 4. Find the scale factor for the dilation of ABCD to A B C D. For Questions 21 and 22, refer to the figure. 21. In J, HK = 28 centimeters and m NK 1 = 72. Find m NJK and the length of NK If radius HJ ++++ measures 20 units, JL = 12, and m HJN = 126.9, find LK, MK, and m MNK A regular hexagon is inscribed in P. Find the area of the shaded region. 24. Find the area of the irregular figure. 2

3 For Questions 25 and 26, refer to the figure. 25. Identify the solid and name its bases. 26. Find the surface area of the solid to the nearest tenth if AB = 8, AC = 25, CF = 14, and EF = Find the lateral area of a rectangular prism with base 4.8 inches by 6.2 inches and height 5.9 inches. 28. The lateral area of a right cylinder is 180.2π square meters and its height is 10.6 meters. Find the radius of the base of the cylinder. 29. Find the surface area of the regular pentagonal pyramid. Round to the nearest tenth. 30. Mark is cutting colored paper to make conical party hats for his daughter s birthday party. He wants to make them with a diameter of 9 inches and a height of 12 inches. What is the lateral area of one party hat? 31. Find the outer surface area of a bowl in the shape of a perfect hemisphere with diameter 36 centimeters. Round to the nearest tenth. 32. Sandra is packing a box with dimensions 54 inches by 78 inches by 42 inches. What is the maximum volume in cubic feet that this box can hold? Round to the nearest tenth. 33. Find the volume of a cone with a radius of 11 inches and a height of 15 inches to the nearest tenth. 34. Which figure has the greater volume, the sphere or the cylinder? 3

4 Chapter 7: Proportions and Similarity 1. Of the 240 students eating lunch, 96 purchased their lunch and the rest brought a bag lunch. What is the ratio of students purchasing lunch to students bringing a bag lunch? A 2:3 B 2:5 C 3:2 D 5:2 2. Demont and Tony are competing to see whose house is taller. Early in the afternoon, Tony, who is 4 feet tall, measured his shadow to be 9.6 inches and the shadow of his house to be 62.4 inches. Later in the day, Demont, who is 5 feet tall, measured his shadow to be 15.6 inches and the shadow of his house to be 62.4 inches. Who lives in the taller house? A Demont B Both houses are the same height. C Tony D There is not enough information. 3. If the triangles are similar, find the value of x. F 8.68 H G J If PQR STU, find the value of x. A 4.4 C 24.6 B 7 D Which expression can you use to find a? F c 8 b 8 H : ; < G 2b c 8 J 2c b 6. If ++++ ST is a midsegment of PQR, which is a true statement? F PQ = 2ST H 3PQ = 4ST G 2PQ = ST J 4PQ = 3ST 7. Name the theorem or postulate that can be used to prove that these triangles are similar. F AA Similarity H SAS Similarity G SSS Similarity J SSA Similarity 4

5 8. Find the value of x so that ST PR. A 4 C 6 B 4 A 8 D 6 A 8 9. ABC JKL with altitudes BX and KY. Find BX. F 19.2 H 24.6 G 21 J Find the value of x. A 4 C 6 B 5 D Ashley wants to make a poster for her campaign from a photograph. She uses a photocopier to enlarge the 4 inch by 6 inch photograph. What are the dimensions of the poster if she increases the size of the photograph by a scale factor of 5? F 2000 inches by 3000 inches H 9 inches by 11 inches G 0.8 inches by 1.2 inches J 20 inches by 30 inches 5

6 Chapter 8: Right Triangles and Trigonometry 1. Find the geometric mean between 7 and 12. A 5 B In PQR, RS = 4 and QS = 6. Find PS. F 2 G 5 C 19 D 2 21 H 10 J Find x. A 3 2 C 4.5 B 14 D 3 4. Find y. F 12 H 9 G 11 J 2 5. If QR ++++ is the hypotenuse of right PQR, PQ = 18, and QR = 24, find RP. A 63 B 2 63 C 30 D 60 For Questions 6 and 7, use the figure to the right. 6. Find QP to the nearest tenth. A 7.5 B12 C18.3 D Find LM. F 5 G 5 3 H 9 J Find HK. A 3 2 B 6 C 6 2 D Which set of measures could represent the lengths of the sides of a right triangle? A 9, 40, 41 C 7, 8, 15 B 8, 30, 31 D 2, 3, Find x to the nearest tenth. A 5.8 C 8.1 B 5.9 D

7 11. Find x to the nearest degree. F 56 H 34 G 45 J Which equation can be used to find x? K F x = y sin 73 H x = G x = y cos 73 J x = LMN OP K NRS OP 13. The Petronas Towers in Kuala Lumpur, Malaysia, are 452 meters tall. A woman who is 1.75 meters tall stands 120 meters from the base of one tower. Find the angle of elevation between the woman s hat and the top of the tower. Round to the nearest tenth. A 14.8 B 34.9 C 55 D A plane flies at an altitude of 350 meters and then starts to descend when it is 6 kilometers from the runway. What is the angle of depression for the descent of the plane? F about 3.3 G about 33.4 H about 8.9 J about Find x to the nearest hundredth. A 4.70 C B D Find r. A about 34.0 C about 11.8 B about 8.9 D about Find the component form of XY %%%%% with X(3, 2) and Y(7, 1). F 4, 3 G 3, 1 H 2, 7 J 10, Find the magnitude and direction of the vector PQ %%%%% for P(6, 5) and Q(0, 13). Round the direction to the nearest tenth. A 12, 22.9 B 8, 33 C 9.5, 16 D 10,

8 Chapter 9: Transformations and Symmetry 1. If A(c, d) is reflected in the y-axis, find the coordinates of A. A A (c, d) B A ( c, d) C A ( c, d) D A (d, c) 2. If ++++ ST with endpoints S(3, 7) and T( 5, 2) is reflected in the line y = x, find the coordinates of S T. A S ( 3, 7) and T (5, 2) C S ( 3, 7) and T (5, 2) B S (3, 7) and T ( 5, 2) D S ( 7, 3) and T ( 2, 5) 3. Given B( 4, 6), under which reflection is B (4, 6)? A reflected in the x-axis C reflected in the line y = 2 B reflected in the y-axis D reflected in the line y = x 4. How many lines of symmetry does a regular decagon have? A 0 B 2 C 5 D Find the magnitude of the rotation of the figure at the right. F 90 H 60 G 74 J Find the image of point A(6, 12) along the translation vector 4, 7. F A'( 4, 7) G A'( 2, 5) H A'(3, 0) J A'(2, 5) 7. What transformation relates CDF and C D F? F reflection G translation H rotation J dilation 8. XY ++++ has the endpoints X( 5, 6) and Y(0, 4). Find the image of XY ++++ under a rotation of 270 about the origin. A X'(6, 0), Y'(4, 5) C X'(2, 3), Y'( 4, 1) B X'(6, 5), Y'(4, 0) D X'(2, 0), Y'( 4, 6) 9. Find the images A( 4, 2) and B( 2, 4) under a clockwise rotation of 90 about the origin. A A ( 2, 4), B ( 4, 2) C A (2, 4), B (4, 2) B A (4, 2), B (2, 4) D A (4, 2), B (2, 4) 8

9 10. What kind of transformation is represented in the figure at the right? A translation C reflection B rotation D dilation 11. What type of dilation occurs with a scale factor of A? U F enlargement H congruence transformation G reduction J glide reflection 12. Sue scans a 4-inch picture into her computer. She stretches the picture s length to 10 inches. Find the scale factor she used. F 6 G V H 2 J 8 8 V 13. The length of the line segment AB is 6 feet. Find the measure of the dilation image A B using a scale factor of 12. F 48 ft G 72 ft H 93 ft J 324 ft 9

10 For Questions 1 3, use O. 1. Name a diameter. A FG ++++ C AB %%%% B AB ++++ D CE %%% Chapter 10: Circles 2. Name a chord. F FO ++++ G AB H AB %%%% 3. Name a secant. A FO ++++ B AB C AB %%%% J CE %%% D CE %%% 4. Find the circumference of a circle with a radius of 26.5 centimeters. F 26.5π cm G 53π cm H π cm J 2809π cm 5. Find the circumference of G. F 9π in. H 15π in. G 12π in. J 30π in. 6. In A, m BAD = 110. Find m DE 1. A 35 C 70 B 55 D In A, m BC 1 = 2x + 16 and m BAC = 5x 98. Find x. A 22 B 27 C 38 D Points D, E, and F are on a circle so that mdef 5 = 210. If K is the center of the circle, what is m DKF? F 210 G 105 H 70 J Chords XY ++++ and WV are equidistant from the center of O. If XY = 2x + 30 and WV = 5x 12, find x. A 58 B 28 C 14 D The diameter of a circle is 34 inches, and a chord of the circle 18 inches. Find the distance between the chord and the center of the circle to the nearest tenth. F 14.4 in. G 15.6 in. H 17.3 in. J in. 10

11 11. What can you assume from the figure? A ABC is isosceles. B ABC is equilateral. C DF = EG D radius of O = x + y 12. If a line is tangent to a circle, then it? is to the radius drawn to the point of tangency. A perpendicular C congruent B parallel D not related 13. Find m C. A 18º C 28º B 25º D 60º 14. Find m 1. A 61 C 82 B 98 D Find x. F 78 H 102 G 90 J Find map1. A 66 C 45 B 57 D Find z. F 2 H 7 G 4.5 J Find ZC. A 4 C 22 B 16 D 32 11

12 19. Which is a true statement if XY ++++ is tangent to P? A ab = bc C a = bc B a 8 = bc D a 8 = b(b + c) 20. Find the center of the circle whose equation is (x + 11) 8 + (y 7) 8 = 121. F ( 11, 7) G (11, 7) H (121, 49) J Find the equation of a circle whose center is at (2, 3) and radius is 6. A (x + 2) 8 + (y + 3) 8 = 6 C (x + 2) 8 + (y + 3) 8 = 36 B (x 2) 8 + (y 3) 8 = 6 D (x 2) 8 + (y 3) 8 = Find the equation of P. F x 8 + (y 3) 8 = 4 H (x 3) 8 + y 8 = 2 G x 8 + (y 3) 8 = 2 J (x 3) 8 + y 8 = 4 12

13 Chapter 11: Areas of Polygons and Circles 1. A square has side length 18 centimeters. Find the area of the square. F 36 cm 8 G 40 cm 8 H 81 cm 8 J 324 cm 8 2. Find the area of the figure. F 76 cm 8 H 88 cm 8 G 80 cm 8 J 92 cm 8 3. Find the area of a rhombus with diagonals that are 24 centimeters and 78 centimeters long. F 234 cm 8 G 468 cm 8 H 936 cm 8 J 1872 cm 8 4. Find the area of parallelogram ABCD. Round to the nearest tenth. A 55.4 m 8 C 69.3 m 8 B 60 m 8 D 80 m 8 5. The area of the parallelogram DEFG is 143 square units. Find the height. Round to the nearest tenth if necessary. F 11 units H 22 units G 14.3 units J 44 units 6. The base of a triangle is three times its height. If the area of a triangle is 54 square inches, find its height. A 18 in. C 3 in. B 6 in. D 1 in. 7. Find the area of quadrilateral PQRS. F 34.1 units 8 H 130 units 8 G 65 units 8 J 360 units 8 8. A trapezoid has a height of 3 meters, a base length of 8 meters, and an area of 30 square meters. What is the length of the other base? A 12 m C 19 m B 11 m D 24 m 13

14 9. Find the area of a regular hexagon with a perimeter of 72 inches. Round to the nearest square inch. F 72 in 8 G 432 in 8 H 374 in 8 J 864 in Find the area of a regular nonagon with a perimeter of 126 inches. Round to the nearest tenth. F in 8 H in 8 G in 8 J in Find the area of the shaded region. Round to the nearest tenth. A 59.1 cm 8 C 25.7 cm 8 B 57.5 cm 8 D 19.6 cm Find the area of a circle with a diameter of 28 meters. F 49π m 8 H 784π m 8 G 196π m 8 J 3136π m If m ACB = 36, find the area of the shaded sector. F 7.9 in 8 H 25 in 8 G 22.5 in 8 J 70.7 in A circular pizza has a diameter of 16 inches. Each slice of pizza has a central angle of 45. What is the area of each slice of pizza? A 3.1 in 8 C 25.1 in 8 B 6.3 in P D in 8 14

15 For Questions 1 and 2, refer to the figure. Chapter 12: Surface Area and Volume 1. Identify the figure. F pyramid G prism H cone J cylinder 2. Identify the shape of a horizontal cross section of the figure. A triangle B ellipse C rectangle D circle 3. The lateral area of a cube is 36 square inches. How long is each edge? F 6 in. G 3 in. H 6 in. J 9 in. 4. Find the surface area of the outside of the open box (no lid). A 1920 in 8 C 752 in 8 B 998 in 8 D 400 in 8 For Questions 5 and67, use a right cylinder with a radius of 3 inches and a height of 17 inches. Round to the nearest tenth. 5. Find the lateral area. F in 8 G in 8 H in 8 J in 8 6. Find the surface area. A in 8 B in 8 C in 8 D in 8 For Questions 7 and 8, refer to the regular hexagonal pyramid. 7. Find the lateral area. F 144 cm 8 H 196 cm 8 G cm 8 J 288 cm 8 8. Find the surface area. A 144 cm 8 B cm 8 C 196 cm 8 D 288 cm 8 15

16 For Questions 9 and 10, refer to the figure. Round to the nearest tenth. 9. Find the lateral area. F 44.0 in 8 G 75.4 in 8 H 88.0 in 8 J in Find the surface area. A 44.0 in 8 B 75.4 in 8 C 88.0 in 8 D in Find the surface area of a square pyramid with a height of 9 centimeters and base with a side measuring 24 centimeters. F 1296 cm 8 G 1806 cm 8 H 2016 cm 8 J 8640 cm Find the volume of a right circular cone with a height of 14 inches and a diameter of 10 inches. Round to the nearest tenth. F in P G in P H in P J in P 13. Find the volume to the nearest tenth. F 168 in P H 344 in P G 252 in P J 504 in P 14. A square pyramid has a height that is 8 centimeters long and a base with sides that are each 9 centimeters long. Find the volume of the pyramid. F 648 cm P G 324 cm P H 216 cm P J 162 cm P 15. Find the volume to the nearest tenth. A m P C 14,476.5 m P B m P D 43,429.4 m P 16

17 16. Find the surface area to the nearest tenth. F m 8 H m 8 G m 8 J m A sphere has a volume of 972π cubic inches. Find the radius of the sphere. A 2 in. B 3 in. C 6 in. D 9 in. 17

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