32 ft. 48 ft. 15 cups 36, 60, 84

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1 Geometry / Geometry Honors Second Semester Study Guide 1. Matthew is 4 feet tall. t 5 o clock in the afternoon, Matthew casts a shadow 20 feet long. He is standing net to a telephone pole that casts a shadow 160 feet long. How tall is the telephone pole? 32 ft 2. The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 128 feet, what is the length of the rectangle? 48 ft 3. salsa recipe uses green pepper, onion, and tomato in the etended ratio 2 : 3 : 4. How many cups of onion are needed to make 45 cups of salsa? 15 cups 4. The measures of the angles of a triangle are in the etended ratio 3 : 5 : 7. What is the measure of each angle? 36, 60, If two triangles are similar, what are the correct proportions for the corresponding sides? 5 cm 8 cm 2 cm 3.2 cm 8 =

2 6. re the triangles similar? If yes, eplain why they are similar. If no, eplain why not No, corresponding angles are not congruent 7. re the two triangles similar? If yes, eplain why they are similar. If not similar, why? H J Yes, by ~ o 39 M o 39 G K 8. What are the values of a and b? 32 a = 8, b = 2 17 a 2 b Figure not drawn to scale.

3 9. Jason wants to walk the shortest distance to get from the parking lot to the beach. Refreshment Stand Jason s Spot on the Beach 18 m 30 m 40 m Parking Lot a: 24 m, b: 32 m a. How far is the spot on the beach from the parking lot? b. How far will his place on the beach be from the refreshment stand? 10. Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen s home and the football field at the eact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 2 miles from her home. The football field is 5 miles from the library. Park Home Library 2 miles 5 miles Football field a: 10 miles, b: 35 miles a. How far is library from the park? b. How far is the park from the football field?

4 11. What is the value of? What is the value of, given that E BD? B or 7 E 5 D 7 C 13. What is the value of? or What is the value of to the nearest tenth?

5 15. D bisects BC, B = 24, BD = 12, and C = 22. What is the value of? C D 12 B 16. Complete the conclusion for the information given below. If you live in Lake Worth, then you live in Palm Beach County. If you live in Palm Beach County, then you live in Florida. Florida If you live in Lake Worth, then you live in. 17. Complete the conclusion for the information given below. If a polygon has four sides then it is a quadrilateral. If a polygon is a quadrilateral, then the sum of the interior angles is 360 degrees. the sum of the int. angles is 360 degrees If a polygon has four sides, then. 18. Complete the conclusion for the information given below. If there is no conclusion, write no conclusion. If a student is late for class, then they serve detention. le was chewing gum in class. No Conclusion

6 19. Complete the conclusion for the information given below. If there is no conclusion, write no conclusion. If a polygon has three congruent sides, then it is a regular triangle. Triangle BC has congruent sides. Triangle BC is a regular triangle. 20. Write a biconditional statement for the given true conditional statement. If two angles have the same measures, then they are congruent. Two angles have the same measure if and only if they are congruent. 21. Write the two conditional statements that form the biconditional below. polygon is a regular pentagon if and only if it has five congruent sides. If a polygon is a regular pentagon, then it has five congruent sides. If a polygon has five congruent sides, then it is a regular pentagon. 22. Classify the triangle with sides given below as right, acute, or obtuse. 4, 8, and 10 5, 12, and 13 btuse Right 23. Find the base of the rectangle shown below If a 25 foot ladder leans against the side of a building 24 feet from its base, how high up the building will the ladder reach? 7 ft 25 24

7 25. Wayne used the diagram to compute the distance from Ferris, to Dunlap, to Butte. How much shorter is the distance directly from Ferris to Butte than the distance Wayne found? Ferris 15 mi 10 miles Dunlap 20 mi Butte 26. What are the lengths of the missing sides in the triangle? 7 Not drawn to scale = 7 2 y 45 = y 7 or Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 10 inches long. What is the side length of each piece? Leave your answer in simplified radical form. 5 2 in. 28. The length of the hypotenuse of a triangle is 4. What is the perimeter of the triangle? Write your answer in simplified radical form. Then rewrite answer to the nearest tenth? ; conveyor belt carries supplies from the first floor to the second floor, which is 24 feet higher. The belt makes a 60 angle with the ground. How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot. 28 ft

8 30. In the triangle below, write the sine, cosine, and tangent ratios for angle B and angle C. B C C Sin B = BC B Cos B = BC C Tan B = B B Sin C = BC C CosC = BC B Tan C = C 31. Viola drives 170 meters up a hill that makes an angle of 6 with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered? m 32. large totem pole in the state of Washington is 100 feet tall. t a particular time of day, the totem pole casts a 249-foot-long shadow. Find the measure of to the nearest degree. 100 ft 22 degrees 249 ft 33. Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree 36 degrees 34. To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44. To the nearest foot, what is the height of the pole? 139 ft

9 35. Draw an image of the translation of BC given by the translation rule (, y) ( 3, y + 5)? y C B C B 36. LaKeesha was sitting in seat J1 at a soccer game when she discovered her ticket was for seat D4. Write a rule to describe the translation needed to put her in the proper seat if the alphabet is the -ais and the numbers are the y-ais. (, y) ( 6, y + 3) 37. Write a translation rule to describe the translation that is 7 units to the left and 1 units down. (, y) ( 7, y 1) 38. The vertices of a triangle are P( 3, 8), Q( 6, 4), and R(1, 1). Name the vertices of the image reflected across the -ais. P '( 3, 8), Q' ( 6, 4), R' ( 1, 1) 39. The vertices of a triangle are P( 2, 4), Q(2, 5), and R( 1, 8). Name the vertices of the image reflected across the y-ais. P '(2, 4), Q'( 2, 5), R'(1, 8) Name the vertices of the image after it is then translated (, y) ( 3, y + 5) P '( 1, 1), Q'( 5, 0), R'( 2, 3)

10 40. Graph the image of triangle XYZ with a center of (0, 0) with and a scale factor of 1/2. y X Y Z 41. The dashed triangle is a dilation image of the solid triangle. What is the scale factor of the dashed to the solid triangle? 8 y 1/ Draw a tessellation using the figure below.

11 43. Which figure can be used to make a tessellation?. B. C. D. 44. How many lines of symmetry does each figure have? Regular Heagon Regular ctagon 45. For each regular polygon shown below, what is the angle needed for rotational symmetry? Point Q is located at (3, -2). Find the coordinates of Q after a 90 degree counterclockwise rotation about the origin y Q (2, 3) Q

12 47. Draw the figure below showing a 90 degree, 180 degree, and 270 degree clockwise rotation about point. B C B C C B C o 90 o 180 B o What is the area of the each triangle below? 3 yd 2 cm 10 yd The figure is not drawn to scale. 5.4 cm The figure is not drawn to scale. 10 ft The figure is not drawn to scale. 15 sq yd 5.4 sq cm 43.3 sq ft 49. The area of a parallelogram is 420 cm 2 and the height is 35 cm. Find the corresponding base. 12 cm 50. Find the area of the trapezoid below. 19 in in in in sq in in.

13 51. Find the area of the trapezoid below. Leave your answer in simplest radical form. 10 ft 60 8 ft How many square feet of material is needed to make each kite shown below? 10 ft 20 ft 3 ft 3 ft 25 cm 4 cm 24 cm 90 sq ft 196 sq cm 53. Find the area of the rhombus below. 8 m 8 m 8 m 8 m 128 sq m

14 54. The side of a regular heagon is 3.7 in. Find the area of the heagon. Round your answer to the nearest tenth sq in. 55. Find the area of a regular heagon with an apothem 16.5 inches long and a side 19 inches long. Round your answer to the nearest tenth sq in. 56. The figures shown below are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second. The figures are not drawn to scale. 15 yd 40 yd : 3 ; 64 : 9 5 : 6 ; 25 : What is the area of a regular decagon with a side of 4 cm? Give the answer to the nearest whole number. 123 sq cm 58. What is the area of a regular pentagon with a side of 10 cm? Give the answer to the nearest tenth. 172 sq cm

15 59. Find the arc measures of B, D, CD and BC in circle below. B o D 3 C o B = 80 degrees D = 100 degrees CD = 130 degrees BC = 50 degrees Find the measures of angles 1, 2 and 3 in circle above degrees ; 2 90 degrees; 3 65 degrees 60. What is the measure of arc XPY? What is the length of arc XPY? Leave your answer in terms ofπ. X 270 degrees; 12π m P 8 m Y 61. rc B has a measure of 150 degrees. What is the length of arc B? What is the area of sector B? Round to the nearest tenth. C 4 m m; 20.9 sq m B

16 62. In circle, what is the eact area of the shaded region? First write your answer in terms of π and simplest radical form. Then simplify to nearest tenth m 192π sq m Hint: To find the area of the shaded segment, subtract the area of the triangle from the area of the sector sq m 63. What is the probability that a point chosen at random from K is on the segmentcj? B C D E F G H I J K 7 / What is the probability that a point chosen at random on the grid will lie in the un-shaded region? Put your answer in simplest terms. 5 / Name the Platonic solid that is shown in the net below. Tetrahedron ctahedron

17 List and sketch all Platonic solids: Dodecahedron Tetrahedron ctahedron Icosahedron Heahedron 66. Use Euler s Formula (F + V= E + 2) to find the missing information below. 12 Faces: Faces: 20 Edges: Edges: Vertices: 20 Vertices: 12 List the number of faces, edges and vertices for each Platonic solid: Heahedron: 6 faces, 12 edges, 8 vertices Tetrahedron: 4 faces, 6 edges, 4 vertices ctahedron: 8 faces, 12 edges, 6 vertices Dodecahedron: 12 faces, 30 edges, 20 vertices Icosahedron: 20 faces, 30 edges, 12 vertices 67. What are the lateral area and the surface area of the prism shown below? 2 m 19 m 6 m 100 sq m; 328 sq m

18 68. Find the lateral and surface areas of the prism shown below. Find the volume of the prism shown below. Round your answer to the nearest whole number m 322 sq m; 332 sq m; 130 cubic m 2 m 26 m 69. Find the lateral and surface areas of the cylinder shown below? Find the volume of the cylinder shown below. Write your answers to the nearest tenth. 14 cm sq cm; 1099 sq cm 18 cm 70. What is the surface area of the cylinder in terms ofπ? 9 in. 20 in. 522π sq in.

19 71. llison is planning to cover the lateral surface of a large cylindrical garbage can with decorative fabric for a theme party. The can has a diameter of 3 feet and a height of 3.5 feet. How much fabric does she need? Round to the nearest square foot. 33 sq ft 72. What is the surface area of the pyramid shown to the nearest whole number? 7 ft 95 sq ft 5 ft 5 ft 73. What is the surface area of the cone in terms ofπ? 17 cm 60π sq cm 3 cm

20 74. What is the slant height of the figures below to the nearest whole number? 19 m 21 m 16 cm 15 cm 10 m 11 cm 11 cm 75. What is the volume of the prism shown below? Round to the nearest tenth if necessary. 17 m 17 cubic m 2 m 1m The volume of a cylinder is 980π in.. The height of the cylinder is 20 in. What is the radius of the cylinder? 7 in.

21 77. What is the volume of the cylinder shown below in terms ofπ? 5 in. 350π cubic in. 14 in. 78. The cylinder below has a volume of Round your answer to the nearest tenth. 3 in. What is the height of the cylinder? 2.4 in. 79. Find the volume of each pyramid shown below? Round to the nearest tenth if necessary. 15 cm 9 ft 11 cm 11 cm 2.75 ft 4 ft 605 sq cm 82.5 sq ft

22 80. What is the volume of the cone shown below as a decimal rounded to the nearest tenth? 26 m 18 m sq m 81. What is the volume of the sphere shown below? Round to the nearest cubic unit. 9 mm 3052 cubic mm The volume of a sphere is 5000π m. What is the surface area of the sphere to the nearest square meter? 3032 sq m

23 83. re the two figures similar? If so, give the similarity ratio of the sides and volumes of the smaller figure to the larger figure. If the figures are not similar, why? Yes; 1 : 3; 1 : What is the similarity ratio of a prism with the surface area of 81 2 m to a similar prism with the surface area of m? 9 : 19 What is the similarity ratio of a sphere with a volume of 8 cm 3 to a sphere with a volume of 64 cm 3? 2 : 4 or 1 : In circle, what is the value of if m = 105? ssume that the lines appear to be tangent are tangent. 75 degrees Figure is not drawn to scale.

24 86. In circle, what is the value of if m P = 12? ssume that the lines appear to be tangent are tangent. P Q 78 degrees Figure is not drawn to scale. 87. satellite is 13,200 miles from the horizon of Earth. Earth s radius is about 4,000 miles. Find the approimate distance the satellite is from the Earth s surface to the nearest mile. The diagram is not to scale miles 13,200 miles 88. Pentagon RSTUV is circumscribed about a circle. RS = 11, SB = 5, CT = 6, CU = 6 UV = 12, and VR = 12. What is the perimeter of RSTUV? R V S 58 B U C T The figure is not drawn to scale.

25 89. In circle ; N P, M N, R P, and M = 3 ft. What is P? R P 1.5 ft M N The figure is not drawn to scale. 90. In circle below, what is the value of? If necessary, round your answer to the nearest tenth The figure is not drawn to scale. 91. In circle below, what is the value of? 25 degrees C B 50 The figure is not drawn to scale.

26 92. In circle below, what is m BC? 57.5 degrees 65 B C The figure is not drawn to scale. 93. The measure of arc DE = 110 and the measure of arc BC = 50. What is the measure of? D B 30 degrees E C The figure is not drawn to scale. 94. What is the value of? If necessary, round your answer to the nearest tenth The figure is not drawn to scale.

27 95. What is the value of? If necessary, round your answer to the nearest tenth The figure is not drawn to scale. 96. What is the value of? If necessary, round your answer to the nearest hundredth. B = 16, BC = 5, and CD = 8 D C 5.13 B 97. Given the diagram of circle below, what is the value of? 0 64 B C 64 degrees D

28 98. low-wattage radio station can be heard only within a certain distance from the station. n the graph below, the circular region represents that part of the city where the station can be heard, and the center of the circle represents the location of the station. Which equation represents the boundary for the region where the station can be heard? 8 y ( + 6) + ( y + 1) 2 = Write the standard equation for a circle with a center (6, 9) and a radius of 3. ( 6) 2 + ( y 9) 2 = Write the standard equation for a circle with a center ( 6, 8), that passes through (0, 0). 2 ( + 6) + ( y + 8) 2 = Construct a line parallel to the given line through the given point that is not on the line. P l

29 102. Construct the perpendicular to the given line at the given point on the line. P l Honors Classes nly 103. Write the resultant of the two vectors as an ordered pair and draw the resultant y , Describe the direction of each shown vector. Find the ordered pair of each vector. N N 65 L W S L E 30 degrees south of east 75 degrees north of east W S , , 62.7 E

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