Geometry 2nd Semester Exam Review Name: Date: Per: Trig & Special Right Triangles 1. At a certain time of the day, a 30 meter high building cast a shadow that is 31 meters long. What is the angle of elevation of the sun? Round to the nearest degree. A. 46 o B. 16 o C. 44 o D. 75 o 2. To secure a tall tree against high winds, support rings are attached to the tree 12 feet from its base. Ropes are used to attach the rings to the anchors on the ground as shown in the figure on the ground as shown in the figure below. Which of the following statements is true? I. The total length of rope used is 28 feet II. The distance between the anchors on the ground is 14 feet III. The length of the longer portion of the rope is 15 feet A. I only B. II only C. III only D. I, II and III 9 ft 13 ft 3. A square has a diagonal of length 12 2 cm. What is the perimeter of the square? P = 4. The arm of a steel crane is 74 feet long. When it is fully extended, the crane arm forms a 30 o angle with a line parallel to the ground. How many feet above the ground is the top of the crane? 74 ft Height above the ground = 9 ft
5. Find the value of x and y. Round to the nearest hundredth when necessary. x y x = 310 m 35 o y = 6. A radio station is going to construct a 6-foot tower for a new antenna on top of their 20-foot tall building. The contractor is standing where the angle of elevation is 40 degrees from his foot to the top of the antenna. Calculate the distance from the antenna to where he is standing. Distance to antenna = 6ft 20ft 40 7. Find the value of x and y. Round to the nearest hundredth when necessary. x 45 o x = 5 m y y = 8. A utility pole breaks and falls as shown. What was the original height of the pole? A. 65 feet D. 18 feet B. 60 feet E. 13 feet C. 30 feet
9. Find the value of x and y. Round to the nearest hundredth when necessary. 20 ft y x = y = x 10. The mainsail on a new sailboat is in the shape of a right triangle as shown. What is the measurement of the smallest angle? Round to the nearest degree. A. 28 o B. 57 o C. 33 o D. 62 o X o 14 ft 26 ft 11. A. If SR = 4 cm, find ST. B. If ST = 15 3 cm, find RT. Round to the nearest hundredth when necessary. A. B. Find x. Round answer to nearest hundredth. 12. 13. 30 x 60 17 m 30 x 60 x = x =
14. The drawing below shows how 3 squares can be joined at their vertices to form a right triangle. What is the area in square centimeters of the largest square? A. 37 cm 2 B. 210 cm 2 C. 420 cm 2 D. 1369 cm 2 12 cm 1225 cm 2 Similarity 15. A size 7 basketball has a circumference of 29.5 inches. A size 6 basketball has a circumference of 28.5 inches. To the nearest hundredth, what is the ratio of the volume of a size 7 basketball to the volume of a size 6 basketball? A. 1.00 B. 1.04 C. 1.07 D. 1.11 16. A model is created to represent a building with a scale of 2 in = 5 ft. What is the height of the model if the projected height of the building is to be 80ft? h = 17. The ratio of the lengths of the sides of two cubes is 2 : 5. The smaller cube is 5 centimeters on one edge. To the nearest whole number of cubic units, what is the volume of the larger cube? A. 391 cm3 B. 782 cm3 C. 977 cm3 D. 1953 cm3 18. The perimeter of rectangle ABCD is 42 inches. The perimeter of a similar rectangle EFGH is 63 inches. What is the ratio of the area of ABCD to the area of EFGH? A. 2:3 B. 3:7 C. 4:9 D. 5:6
19. Which triangles must be similar? A. two obtuse triangles B. two scalene triangles with congruent bases C. two right triangles D. two isosceles triangles with congruent vertex angles 20. The cylinders to the right are similar. Complete the table of ratios. 12m 7m Small Large Scale Factor Area of Base Circumference of Base Surface Area Lateral Area Volume 21. The figure to the right shows two similar polygons. What is the value of y? A. 6 B. 7 C. 8 D. 9 22. In the figure below, MNR is similar to MPQ. What is the value of x? A. 7.5 B. 10 C. 21 D. 30
23. Find the missing side lengths. 6 8 x y 12 x = y = 25 24. The ratio of vanilla ice cream cones to chocolate ice cream cones sold in a local ice cream store is 4:9. If 299 vanilla and chocolate cones were sold in one day, how many of them were chocolate? Chocolate Cones = Polygons Fill in the equations below: 25. SUM of interior angles of a convex polygon: 26. EACH interior angle of a regular convex polygon: 27. SUM of exterior angles of a convex polygon: 28. EACH exterior angle of a regular convex: Identify each quadrilateral from its figure. 29. 30. 31. 32. 33. 34.
Tell whether each statement is sometimes, always, or never true. 35. A rectangle is a parallelogram. Always Sometimes Never 36. A parallelogram is a rhombus. Always Sometimes Never 37. A rectangle is a quadrilateral. Always Sometimes Never 38. A square is a rectangle. Always Sometimes Never 39. An isosceles trapezoid is a parallelogram. Always Sometimes Never 40. The sum of the measures of the interior angles of a regular polygon is 540 degrees. What type of polygon is this? Polygon = 41. If the ratio of one interior angle of a polygon to one exterior angle is 3:2. What is the polygon? Polygon = 42. In parallelogram ABCD angle ABC is equal to 2x + 60 and angle ADC is equal to 5x. What is the measure of each angle? m A A D C B m B m C m D 43. I am a regular polygon. My diagonals are congruent, they bisect each other, and form a 90 degree angle when they intersect. Also, all my angles are 90 degrees. What am I? Polygon Type = 44. If the exterior angles of a polygon are given as 4x, 7x, 5x, and 8x, what is the value of x? x =
45. The coordinates of a quadrilateral are P(1, -3), Q(-4, 2), R(-1, 5), and S(4, 0). What is the most appropriate classification for this quadrilateral? Type of Quadrilateral = 46. In rhombus PQRS, PQ = 3a + 7 and QR = 4a - 11. What is the value of a? P Q a = S R 47. If m SPQ a 2 27 o and 2 m PSR 2a 54 o, find the value of a so that PQRS is isosceles. P Q a = S R Area and Perimeter 48. To the nearest tenth of a square inch, what is the area of an equilateral triangle with a side length of 6 inches? A. 31.2 in2 B. 18.0 in2 C. 15.6 in2 D. 12.7 in2 49. Find the circumference of a circle with an area of 36 yd2. Leave answer in terms of. C =
50. A fence around a square garden has a perimeter of 48 feet. Find the approximate length of the diagonal of this square garden. A. 12 ft B. 17 ft C. 21 ft D. 24 ft 51. The side length of an equilateral triangle is 14 inches. To the nearest tenth of a square inch, what is the area of the triangle? A. 340 in2 B. 97.0 in2 C. 84.9 in2 D. 49.0 in2 14 in 52. The floor of a gazebo forms a regular octagon. The approximate area of the floor is 174 m2.the length of a side of the octagon is 6 meters. Which answer is closest to the length of the apothem of the octagon? A. 4.67 meters B. 5.35 meters C. 6.88 meters D. 7.25 meters 53. To the nearest square inch, what is the surface area of a right cylinder with radius of 3 inches and height of 18 inches? A. 198 in2 B. 283 in2 C. 396 in2 D. 509 in2
54. What is the area of isosceles trapezoid ABCD? A. 62.5 square units B. 75.0 square units C. 76.4 square units D. 150 square units Use the given rectangle for # 55 & 56. (3x + 5) cm 2x cm 55. Which expression represents the perimeter of this rectangle? A. (6x + 5) cm B. (10x + 10) cm C. (5x + 5) cm D. (5x + 10) cm 56. Which expression represents the area of this rectangle? A. (6x + 10) cm 2 B. (6x 2 + 10) cm 2 C. (5x 2 + 10x) cm 2 D. (6x 2 + 10x) cm 2 57. Find the area and perimeter of the given parallelogram. 13 12 Perimeter = Area = 20
58. The diagram shows a hexagon drawn inside a rectangle. What is the area of the hexagon? A. 21 cm 2 B. 24 cm 2 C. 30 cm 2 D. 54 cm 2 Polyhedrons 59. Given that a cone has a volume of 936 cm2 and the height is 10 cm, what is the radius of the cone? r = For # 60 & 61, use the pyramid provided. 60. In the figure below, the pyramid is a right pyramid with a square base. Which of the following represents its surface area? A. 1040 m2 B. 1240 m2 C. 1440 m2 D. 2480 m2 61. What is the volume of this pyramid? V = 62. Using the two cubes below, choose the answer that would represent the ratio of their SURFACE AREAS A. 1:3 B. 3:6 C. 1:9 D. 1:6 1 in 3 in
63. Amanda is wrapping a box that is 38.1 cm long, 8 inches wide and 4 inches high. If 1 inch = 2.54 cm, and she has 1100 cm3 of wrapping paper, will she have enough wrapping paper? Circle Yes or No 64. Use the cylinder shown. Given that the radius is 4 cm and the height is 10 cm, which answer represents the volume? A. 160π cm 3 B. 640 π cm 3 C. 16 π cm 3 D. 80 π cm 3 65. Match the following name to the polyhedron: pentagonal prism cylinder rectangular prism triangular prism tetraheron a) b) c) d) e) 66. A Right Triangular Prism is shown below. What is the lateral surface area of this triangular prism? S L = 18 cm 46 cm 24 cm 67. Find the volume of the Right Triangular Prism above in #66. V =
68. Which polygon is convex, and which is concave? 69. Given that a sphere has a volume of 1214 in 3, find the radius of the sphere. Round to the hundredth. r = 70. Find the area of an equilateral triangle whose edges are 14 cm. A = Use the figure below shows a draft drawing of a toy rocket to answer # 71-73. The bottom of the rocket has already been painted with flame resistant paint, and does not need any additional paint. 71. If you were to paint the available portions of the rocket, what would you be painting? (Think, lateral area, or surface area of each portion.) 12 cm 72. Write the formula for the top part of the rocket. Find the top portion of the rocket. (Don t forget the slant height.) Formula = 24 cm S L = 73. Write the formula and find the bottom portion of the rocket. Then find the total amount of paint needed. 9 cm Formula =
S T = Circles Fill in the blanks with the appropriate word or example using correct notation. 74. Name a secant:. 75. Name a tangent:. 76. Name a major arc:. 77. 78. CD is a(n). DCB is a(n). D G C E A H F 79. CB is a(n). 80. Name an inscribed angle. :. B 81. Name a central angle. :. 82. In the figure below, NP is a diameter of R. What is the measure of NM? mnm = 83. If a tangent and a chord intersect at a point on a circle, what do you know must be true about the measures of the two angles that are formed? Use the diagram to the right. A. They each measure one half the difference of the measures of their intercepted arcs. B. Their measures are one half the measures of their vertical angles. C. They are supplementary. D. Their measures equal the measures of their intercepted arcs. 84. In the figure below, what is the value of a in the figure to the right? A. 9 B. 12 C. 12.75
D. 13.5 85. To the nearest tenth, what is the length of AB in C? Length of AB = 86. Find y and RU in F. N F R y = 5y - 28 3y RU = 87. In C, what is the measure of major arc DGF? U mdgf = E is the center of the circle. AB CD. The diagram is not necessarily drawn to scale. 88. If mbad 225 and m 2 105, 89. If mab = 5x 15 and mcd = 3x 1. then find mad. find the value of x. A E 1 2 B C A E 1 2 B C D mad = D x =
Transformations 90. Rectangle R S T V is a dilation of rectangle RSTV. What is the scale factor of the dilation? A. 1 3 B. 1 2 C. 2 y 7 6 5 4 3 2 1 R S -5-4 -3-2 -1 1 2 3 4 5 6 7 8 9 10 11-1 -2-3 -4-5 R S V T V T x D. 3 Tell which transformation (reflection, rotation, translation, dilation) if any, are shown below. 91. 92. 93. 94. 95. Find the scale factor for the dilations shown. Image is shaded. 5 cm 2 cm k =
For # 96-99 use the graph below to perform the following transformations. Use a different colored pencil for each transformation. Start with #96 and go in order. 96. Draw a trapezoid in the second quadrant. Use BLACK. P: (-6, 5) Q: (-6, 2) R: (-3, 7) T: (-3, 0) 97. Translate the hexagon using the following rule: ( x 9, y 9) Draw and label on graph using RED. Record the new points: P (, ) Q (, ) R (, ) T (, ) y 9 8 7 6 5 4 3 2 1-19 -18-17 -16-15 -14-13 -12-11 -10-9 -8-7 -6-5 -4-3 -2-1 -1 1 2 3 4 5 6 7 8 9-2 -3-4 -5-6 -7-8 -9-10 -11-12 -13-14 -15-16 -17-18 -19 x 98. Rotate the trapezoid 90 clockwise about the origin. Draw and label on graph using GREEN Record the new points: P (, ) Q (, ) R (, ) T (, 99. Dilate the image using a factor of 2 from the origin. Draw and label using BLUE Record the new points: P (, ) Q (, ) R (, ) T (, )