Lincoln Public Schools. Geometry. Semester Two Review CALCULATOR. 1. If X(5,4) is reflected in the line y = 2, then find X.
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1 1. If X(5,4) is reflected in the line y = 2, then find X. Lincoln Public Schools Geometry Semester Two Review LULTOR. (5,2). (5,0). (-1,2) D. (-1,4) 2. is rotated 90 counterclockwise. What is its image? y D 4. EF H 2 D. GH G F -2 E -4 D 3. Use the translation (,y) ( + 6, y 5). What is the preimage of (3,-2)?. (9,-7). (3,3). (-3,3) D. (-7,9) -6-8
2 4. D ~ WXYZ. Find the scale factor of D to WXYZ.. 1:1. 2:3. 3:2 D. 9:8 W X 4 8. Find E D D 6 4 E D Z Y 5. Given PQR and STU with PQ = 20, QR = 25, m Q = 56, ST = 15, UT = 12, US = 18, and m T = 56. Find PR D Identify the dilation and its scale factor. 5. Reduction, 8 8. Reduction, 5 5. Enlargement, 8 8 D. Enlargement, 5 16 P P 6. Which postulate or theorem proves the triangles are similar?. Similarity. S Similarity. SS Similarity D. SSS Similarity Find the value of D omplete the proportion. 7. Find the value of y D y RM =? TM M. TM. RT. T R T M D. M
3 12. Find the value of. 16. Find the tangent of angle X. Round your answer to four decimal places D D Z X 8 Y 13. Find the value of D Find mhmk D. 240 M L 40 G 60 H J K 14. Which numbers can represent the lengths of the sides of a right triangle? 18. Find the value of.. 3, 9, 89. 4, 7, 67. 5, 8, 89 D. 6, 6, D Find the value of D Find the value of D
4 20. Find DE. 24. Find the area of the regular polygon D D E. 6 2 m m m 2 D. 72 m 2 6 m 3 2 m 21. Find the value of D Find the sum of the eterior angles of a regular octagon D If m POQ is 45 and the diameter is 20 m, find the length of PQ.. 2.5π m. 5.0π m. 15π m D. 17.5π m 26. The radius of a circle is 23 mm. Find the circumference of the circle. Use 3.14 for π. P 20 m O 45 Q 23. Find the area of Δ cm mm mm mm cm 2 15 cm D mm cm 2 D cm 2
5 27. Find the area of the circle.. 6π cm 2. 12π cm 2. 36π cm 2 D. 144π cm 2 12 cm 30. What is the area of the label on a soup can that is 4 inches tall and has a radius of 1 inch?. 4π in. 2. 6π in. 2. 8π in. 2 D. 16π in Find the area of the shaded region.. 92 in in in. 2 D. 908 in Find the probability that a randomly chosen point in the figure lies in the shaded region D in Find the surface area of the right prism.. 60 units units units 2 D. 164 units Find the surface area of the square pyramid. 1 Use the formula S = + Pl m m m 2 D. 580 m 2 m 12 m
6 33. Find the surface area of the right cone. Use the formula S = πr 2 + πrl. Use π = Round your answer to the nearest whole number. 36. Find the volume of a square pyramid with a base area of 40 square inches 1 and a height of 9 inches. V = h ft ft ft. 2 D. 452 ft. 2 8 ft. 6 ft. ft cubic inches. 180 cubic inches. 360 cubic inches D cubic inches 34. Find the volume of the right cylinder. Use π = V = π r 2 h. Round your answer to the nearest whole number. 37. Find the surface area of the sphere. Use the formula S = 4πr 2. Round your answer to the nearest whole number.. 70 cm cm cm 3 D. 99 cm 3 5 cm 14 cm. 28 in in in. 2 D. 452 in. 2 3 cm 35. Find the volume of the cone. Use the formula V = 1 π r 2 h. 3. 5π cm 3. 12π cm 3 5 cm. 15π cm 3 D. 36π cm 3 3 cm Find the volume of the sphere. V = π r π cm π cm 3 9 cm. 1296π cm 3 D. 7776π cm foot building casts a 70-foot shadow. t the same time, a tree casts a 14-foot shadow. How tall is the tree?. 20 ft.. 30 ft.. 44 ft. D. 64 ft.
7 40. The perimeter of a square is 64 cm. Find the length of a diagonal. 44. Find the value of a.. 8 cm cm. 16 cm D cm D a rectangular yard is 50 feet wide by 120 feet long. How far is it diagonally from one corner to the opposite corner? 45. Find the value of.. 65 ft.. 85 ft ft. D. 170 ft D ΔGHI is equilateral with sides measuring 12 m. Find GJ. G. 6 m. 6 3m 12 m. 12 m D. 12 3m I J H 46. Use the origin as a dilation with scale factor k = 1 to find the coordinates 4 of the image of (-16, 20).. (-4,5). (4,-5). (-5,4) D. (5,-4) 43. Find the value of and y.. = 5, y = 5 3. = 5 3, y = 5. = 5, y = 5 2 D. = 5 2, y = 5 y Find the value of t D t
8 48. Find the cosine of angle Which two quadrilaterals could be similar?. LMNP ~ VWXY. LMNP ~ QRST T. QRST ~ VWXY D. QRST ~NMLP L Q 6 R 8 M S Y V W X D. 5 4 P 20 N 49. If Δ GHI ~ Δ JKL then what is the m H?. 30 G D H L I 20 K J 53. Find the value of and y.. = 60, y = 0. = 80, y = 120. = 0, y = 60 D. = 120, y = 80 y ramp is used to unload trucks. How high is the end of a 48 foot ramp when it is tipped by a 34 angle? ft ft ft. 48 ft. 54. Find the value of a.. a = 40. a = a D ft. 34. a = 0 D. a = You are measuring the height of a building. You stand 140 feet from the base of the building. You measure the angle of elevation from a point on the ground to the top of the building to be 42. Estimate the height of the building.. 93 ft.. 4 ft ft. D. 155 ft ft. 55. Find the length of D.. 3π in.. 6π in.. 12π in. D. 16π in. 8 in. 135 D
9 56. The radius of the large circle is 12 cm. The radius of each of the small circles is 3 cm. Find the probability that a randomly chosen point in the figure lies in the shaded region Find the surface area of the cylinder. S = 2πr 2 + 2πrh. 16 cm cm cm cm 2 20 cm. D cm D What is the probability that a point selected randomly on F is on E? D E F One end of a dog s leash is attached to a stake in one corner of the backyard where two sides of the fence meet. If the leash is 12 feet long, what is the maimum area the dog can use? Round your answer to the nearest foot ft ft ft. D. 452 ft. 12 ft D Find the probability that a point chosen at random is inside the square but outside the semicircle %. 25.0%. 50.0% D. 60.7% 6 in. 61. Find the area of the shaded ring if QP = 8 inches and QR = 12 inches.. 16π in 2. 64π in 2. 80π in 2 D. 144π in 2 Q P R 6 in.
10 62. Find the measure of each interior angle of a regular octagon D What is the sum of the measures of the angles in a pentagon? D Find the volume of a pyramid that has a square base with 5 cm sides and a height of 9 cm. V = 1 3 h. 15 cm cm cm 3 D. 75 cm Find the volume of the hemisphere. The formula for the volume of a 4 3 sphere is V = π r. Use π = Round your answer to the nearest 3 whole number. 64. In circle, find the value of D. 180 (3) m m 3 12 m m 3 D m Find the radius of a circle with circumference 20π cm.. cm 65. Find the value of a.. 5π cm cm D. π cm. 80 D a 69. Find the radius of a circle with area 81π ft 2.. 9π ft.. 18 ft.. 3π ft. D. 9 ft.
11 70. Find m JL D. 244 K (3 + 11) (2 + 48) J L OPEN-ENDED QUESTIONS 73. Rewrite the fraction so that the numerator and denominator have the same units. Then simplify. a) 4ft. 12in. b) 70 cm 1m 74. Find the geometric mean of the two numbers. 71. Given: D. Which two steps prove Δ Δ D? a) 5 and 20 b) 2 and 40., Similarity. D D, S Similarity 75. The diagonal of a square is 12 cm. Find the perimeter and area.., SS Similarity D. D D,SSS Similarity D 12 cm 75. perimeter: area: suur suur 72. andd are tangent to circle. Find the value of.. = = 5. = D. = 9 D 76. Find the volume. a) b) 12 m 5 m 4 m 3 ft. 12 ft. a) b) 77. The volume of the right prism is 160 cubic centimeters. Find the value of. cm 77. = 2 cm
12 78. Line k is tangent to the circle. Find m k m 1 = 82. The volume of the cylinder is 3817 m 3. Find the radius r. V = π r 2 h. Round your answer to the nearest whole number. r 82. r = 15 m 79. Line k is tangent to the circle. Find m k 79. m 2 = Find the surface area and volume of the right prism. m 83. S = Volume = 80. The two polygons are similar. Find the ratio, shaded to unshaded, of the perimeters and of the areas. 7 m 3 m perimeters: areas: 84. Find the surface area and volume of the cube. 84. S = 81. ount the number of faces, verticies and edges of the polyhedron. 81. faces: verticies: edges: 8 in. Volume =
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