4.! ABC ~ DEF,! AC = 6 ft, CB = 3 ft, AB = 7 ft, DF = 9 ft.! What is the measure of EF?
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1 Name:!!!!!!!!!!!!! Geo(2) GEOMETRY (2) REVIEW FOR FINAL EXAM #2 1. If ABC is similar to ADE, then AB AD =? AE. Which replaces the? to make the statement true? A. AC!! B. AE!! C. DE!! D. BC 2. In ABC, <A is a right angle, <B = 60. IF BC = 10 ft., then AB = A. 10 ft!! B. 5 ft.!! C. 5 2 ft.!! D. 5 3 ft. 3. What is the exact perimeter of ABC, if <A = 90, <B = 45 and AB = 5 ft? A ft!! B. 15 ft.!! C ft.!! D ft. 4.! ABC ~ DEF,! AC = 6 ft, CB = 3 ft, AB = 7 ft, DF = 9 ft.! What is the measure of EF? A. 21 2!! B. 15 2!! C. 9 2!! D What is the length of the unlabeled side in the picture below? 14 ft 16 ft 24 ft 20 ft A.! 10 ft.!! B. 11 ft.!! C. 12 ft.!! D. 13 ft.
2 6. ABCD is a rhombus. A = (0, 0); B = (3, 4); D = (5, 0) What are the coordinates of vertex C? A. (5, 4)!! B. (6, 4)!! C. (8, 4)!! D. (4, 3) 7. FRED is a parallelogram. F = ( -1, 4); R = ( 3, 8); D = (5, 0) What are the coordinates of E? A) (-3, 12)! B (-1, 4)!! C (1, 4)!! D. (9, 4) 8. A, D, C are points on circle O such that <ADC = 28. What is the measure of AC ª? A. 7!! B. 14!! C. 28!! D The figure below shows a right circular cone on top of a hemisphere with the same radius. To the nearest whole number, what is the volume of this solid? 4 cm 4 cm A. 201 cm 3!! B. 56 cm 3!! C. 278 cm 3!! D. 309 cm 3! 10. A cylindrical water container is 1.2 meters high and has a diameter of 4.6 meters. Approximately how many cubic meters of water will the container hold when it is half full? A. 4.33!!! B. 9.97!! C !! D
3 11. ABC ~ LMN! AB = 5 ft; AC = (x + 5) ft; BC = (x + 4) ft! LM = 10 ft; LN = (3x + 3) ft; MN = (3x + 1) ft. What is the length of AC? A. 11 ft!! B. 12 ft.!! C. 22 ft.!! D. 24 ft. 12. In ABC <A is a right angle, <B = 45. AC = 6 ft, what is the length of BC? A. 6 ft.!! B. 6 2 ft.!! C. 6 3 ft.!! D. 12 ft. 13. Which figure has all sides of equal measure, but not necessarily all angles of equal measure? A. Square! B. Rectangle!! C. Rhombus!! D. Trapezoid 14. B, R, and D are points on circle O such that < RBD = 34. What is the measure of <ROD? A. 17!! B. 34!! C. 56!! D DEFG is a rhombus with m<efg = 28. What is the measure of <GDE? A. 14!! B. 28!! C. 30!! D A rectangular rug is 24 ft by 10 ft. A rhombus design is formed inside the rug by joining the midpoints of each side of the rectangle. What is the length of each side of the rhombus? A. 13 ft.!! B. 26 ft.!! C. 169 ft.!! D. 240 ft.
4 17. A woman who is 6 feet tall casts a shadow that is 4 feet long. At the same time a nearby flagpole casts a shadow that is 18 ft. long. How tall is the flagpole? A. 10 ft.!! B. 12 ft.!! C. 22 ft.!! D. 27 ft. 18. A cone has a slant height of 10 cm with a lateral area of 60$ cm 2. What is the volume of a sphere with a radius equal to that of the base of the cone? A. 102$ cm 3!! B. 144$ cm 3!! C. 288$ cm 3!! D. 1333$ cm 3! 19. The measure of an angle inscribed in a semicircle is: A. 45º!!! B. 90º!!! C. 180º!!! D. cannot be determined 20. Which statement about a parallelogram must be true? A. All of its sides are the same length. B. Its diagonals are the same length. C. Its opposite angles have the measure. D. At least one angle is a right angle. 21. What is the volume of the figure below: 9 in. 10 in. 6 in. A. 86$ in 3! B. 104$ in 3!! C. 117$ in 3!! D. 171$ in 3!
5 22. An open area at LS is in the shape of a quadrilateral. Two sidewalks crisscross this open area as diagonals of the quadrilateral. If the walkways cross at their midpoints and the walkways are equal in length, which of the descriptions below is the best for the shape of the open area? A. parallelogram!! B. rhombus!! C. rectangle!! D. trapezoid 23. A sector of a circle is formed by a central angle of measure 60. If the diameter of the circle is 6 inches, what is the area of the sector? A. 1.5$ in. 2!! B. 2$ in. 2!! C. 6$ in. 2!! D. 8$ in. 2!! 24. The bases of a prism are right triangles with legs 3 in and 4 in. The height of the prism is 6 in. What is the surface area of the prism? A. 72 in. 2!! B. 84 in. 2!! C. 96 in. 2!! D. 108 in. 2!! 25. In circle O with diameter AC, the measure of BC ª = 60. What is the measure of < ABO? A. 20!! B. 30!! C. 40!! D Given ABC with right <B. If AB = 10 ft and AC = 24 ft, then the measure of <A to the nearest degree is: A.! 23!! B. 25!! C. 65!! D What is the equation of the circle with center (3, -5) and radius 10? A. (x 3) 2 + ( y 5) 2 = 10!!! B. (x 3) 2 + ( y + 5) 2 = 10!! C. (x 3) 2 + ( y 5) 2 = 100!! D. (x 3) 2 + ( y + 5) 2 = 100!!
6 OK LET S GET SERIOUS!!! 28.! a) What is the area of a regular pentagon! inscribed in a circle of radius 20 ft?!!!!!!!!!!!!!!! [to the nearest foot]!! b) What is the perimeter of the same pentagon?!!!!!!!!!!!! [to the nearest foot]! 29.! a) What is the area of the isosceles trapezoid TRAP with base TR = 34 ft,!! if PA = 18 ft and < TRA = 40?!!!!!!!!!!!! [to the nearest foot]!! b) What is the perimeter of the same trapezoid?!!!!!!!!!!!! [to the nearest foot]! 30. Rhombus FRED with FE = 12 ft. and DR = 16 ft.! a. Exact area of FRED?!!! b) Exact perimeter of FRED?!!! c) <R = to the nearest tenth of a degree.
7 31. Given circle O with diameter AB has radius 5 ft.! Chord CB has length 8 ft.! a) What is the measure of AC ª to the nearest degree?! b) To the nearest foot what is the length of CB ª? 32. What is the equation of the circle with the endpoints of a diameter at (2, 9) and (8, 13)?!!!!!!!!!!!! 33. MARY is a parallelogram. <M = (x 2 ) and <R = (3x + 18). What is the measure of <A?!!!!!!!!!!!! 34. C and D are points on circle O so that <COD = 40.! The radius of O is 10 ft.! a) To the nearest tenth, what is the area of the segment of O cut off by CD.! b) To the nearest tenth, what is the perimeter of the segment of O cut off by CD.
8 35. In circle O below, AB ª = 70, <EOD = 130. E A B <D = O <BFC = F BC ª =! D C 36.!!!!!!!! What is the volume?!! 6!!!!!! What is the lateral area? 5 8!!!!!!!! What is the total surface area? 37. In parallelogram ABCD, AB = (2x + 3y) BC = (5x + 2y) CD = 19 and AD = 31. Find x and y.!!!!!!!!!!!! x =!!!!!!!!!!!!! y =
9 38. Give the most descriptive name that you can for each quadrilateral: 39. Solve for x.!!!!!! x = 40. PSRQ is an inscribed quadrilateral. PSR º = 97º. Find the measure of S. P S R! Q
10 41. Always, Sometimes, or Never.! If you answer sometimes, give an example for when it is true and an example for when it is not true. a) A rhombus is a square. b) A square is a parallelogram. c) Both pairs of opposite sides of a trapezoid are parallel. d) The diagonals bisect the angles of a parallelogram. e) A rhombus is a rectangle. f) The diagonals of a kite bisect each other. g) The legs of a trapezoid are congruent. h) If FGIJ is an isosceles trapezoid, then < F is supplementary to < I. i) If the diagonals of a parallelogram are congruent, it is a square. j) The diagonals of a parallelogram are perpendicular. k) If one angle of a parallelogram is right, the parallelogram is a rectangle. l) The diagonals of a trapezoid bisect each other. 42. In circle O, AB is a diameter, and AB P CD. If CD ª = 108 and AE ª = 2BE ª What is the measure of <AME?
11 43. What is the lateral area of a cylinder of height 10 feet and volume 320$ ft 3?!! 44. From a point 50 feet from the base of a flagpole the angle of elevation to the top of the pole is 40. How tall is the flagpole? (to hundreds place) 45. What is the area of rhombus FRED if FE = 12 ft, and RD = 10 ft?!!!!! What is the perimeter of FRED? 46. What is the best name for quad ABCD. Be sure to show the slope work that helped you decide. A(-3,8) B(0,4) C(8,10) D(5,14)
12 47. Solve for x.!!!!!!!!!! x = G x F C 3 6!! R 15 T 48. Sketch a cylinder with a base radius of 5 and a height of 8 feet.!!!!!! a) What is the exact volume of the cylinder?!!!!!! b) What is the exact lateral area of the cylinder?!!!!!! c) What is the exact total surface area of the cylinder? 49. Find all the missing sides and angles !!!! 50. Find the total area of the following shape:!
A. 180 B. 108 C. 360 D. 540
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