# Geometry Honors Final Exam REVIEW

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1 Class: Date: Geometry Honors Final Exam REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine whether the quadrilateral is a parallelogram. Justify your answer. a. Yes; Opposite angles are congruent. b. No; Opposite angles are congruent. c. Yes; Consecutive angles are not congruent. d. No; Consecutive angles are not congruent. 2. In rhombus QRST, if QR =18, find ST. a. 9 c. 18 b. 36 d For trapezoid ABCD, E and F are midpoints of the legs. Let GH be the median of ABFE. Find GH. a. 42 c b d. 29 1

2 Determine whether each pair of figures is similar. Justify your answer. 4. a.!def "!BAC because the corresponding angles of each triangle are congruent. The ratio of the corresponding sides is 1. b.!def is not similar to!bac. The ratios of the corresponding sides are not the same. c.!def is not similar to!bac. Corresponding angles are not the same. d.!def "!ABC because the corresponding angles of each triangle are congruent. The ratio of the corresponding sides is 2. Find x and the measures of the indicated parts. 5. BD and CE BD = 4x CE = 2x + 2 a. x = 5, BD = 20, CE = 12 c. x = , BD =, CE = b. x = 5, BD = 20, CE = 8 d. x = 3, BD = 12, CE = 20 2

3 6. Find the measure of the BD. a c. 2 6 b. 135 d Find x and y. a. x = 30, y = 17.1 c. x = 45, y = 17.1 b. x = 45, y = d. x = 30, y =

4 Graph each figure and its image under the given translation. 8. AB with endpoints A(#3, 2) and B(#4, 3) under the translation left two units and down one unit a. c. b. d. 4

5 Copy parallelogram ABCD. 9. Rotate the parallelogram 90 clockwise about point Q. a. c. b. d. 10. a. 3; enlargement c. b. 3; reduction d. 1 3 ; enlargement 1 3 ; reduction 5

6 The radius, diameter, or circumference of a circle is given. Find the missing measures. Round to the nearest hundredth if necessary. 11. d = 27.9 mm, r =?, C =? a. r = 55.8 mm, C = mm c. r = mm, C = mm b. r = 55.8 mm, C = mm d. r = mm, C = mm 12. Find the exact circumference of the circle. a. 5\$ in. c. 7\$ in. b. 10\$ in. d. 4\$ in. 13. In ña, AC % AF and AE = 5. Find meg. a. 7 c. 8 b. 6 d. 5 6

7 Find x. Assume that any segment that appears to be tangent is tangent. 14. a. 10 c. 12 b. 5 d. 15 Find x. Round to the nearest tenth if necessary. 15. a. 6 c. 4 b. 5 d. 3 7

8 Graph the equation. 16. (x # 1) 2 + (y + 2) 2 = 25 a. c. b. d. 17. Find the area of the figure. Round to the nearest tenth if necessary. a. 864 yd 2 c. 432 yd 2 b. 216 yd 2 d. 60 yd 2 8

9 Find the area of the figure. Round to the nearest tenth if necessary. 18. a units 2 c. 192 units 2 b. 624 units 2 d units 2 Find the lateral area of each prism. Round to the nearest tenth if necessary. 19. a. 162 units 2 c. 210 units 2 b. 186 units 2 d. 224 units 2 Find the surface area of each prism. Round to the nearest tenth if necessary while doing your calculations as well as in your final answer. 20. a. 586 units 2 c. 456 units 2 b. 552 units 2 d. 360 units 2 9

10 Find the slant height of the cone with the given measurements, rounded to the nearest hundredth. Then use your result to find the surface area of the cone. Use 3.14 for \$. Round the final answer to the nearest ten-thousandth. 21. height: 11 yards diameter: 16 yards a yards 2 c yards 2 b yards 2 d yards 2 Find the volume of the cylinder. Use 3.14 for \$. Round to the nearest tenth. 22. a in 3 c in 3 b in 3 d in 3 Find the volume of the pyramid. Round to the nearest tenth if necessary. 23. a in 3 c. 14,400 in 3 b in 3 d. 11,520 in 3 10

11 Refer to Figure 1. Figure Name a line that contains point J. a. DB & c. n b. GF & d. p 25. What is another name for line n? a. line JB c. '(( GF & b. '(( DC & d. AC 26. Name a point NOT contained in '(( AD & or '(( FG &. a. K c. H b. A d. D 11

12 Refer to Figure 2. Figure Name four points that are coplanar. a. G, D, L, B c. L, A, C, G b. C, K, A, G d. K, B, D, L 28. Name an intersection of plane GFL and the plane that contains points A and C. a. line LC c. line AC b. C d. plane CAB 29. Find the value of the variable and GH if H is between G and I. GI = 6b + 1, HI = 4b # 2, HI = 14 a. b = 4, GH = 11 c. b = 2.17, GH = b. b = 1.5, GH = 10 d. b = 4, GH = 25 Find the coordinates of the midpoint of a segment having the given endpoints. 30. Q Ê Ë #8, 10 Ê ËÁ 8, 6 ˆ a. Ê Ë 0, 8 c. Ê ËÁ #16, 4 ˆ b. Ê Ë 1, 7 d. Ê ËÁ #8, 2 ˆ 12

13 In the figure, KJ (( & and KL (( & are opposite rays. )1 % )2 and KM ((& bisects )NKL. 31. Which is NOT true about KM? a. )MKJ is acute. b. )3 % )MKL c. Point M lies in the interior of )LKN. d. It is an angle bisector. 32. If m)nkl = 82 and m)mkn = 3s + 2, what is m)4? a c. 41 b. 13 d The measures of two complementary angles are 12q # 9 and 8q Find the measures of the angles. a. 42, 48 c b d. 96, 84 Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular. 34. a. pentagon, convex, regular c. hexagon, convex, regular b. hexagon, concave, regular d. hexagon, convex, irregular 13

14 Find the length of each side of the polygon for the given perimeter. 35. P = 100 ft. Find the length of each side. 36. a. 41 ft, 41 ft, 17 ft, 17 ft, 24 ft c. 50 ft, 50 ft, 20 ft, 20 ft, 30 ft b. 29 ft, 29 ft, 13 ft, 13 ft, 16 ft d ft, 33.5 ft, 14.5 ft, 14.5 ft, 19 ft Find the volume of the solid. a. 84 unit 3 c. 30 unit 3 b. 42 unit 3 d. 96 unit 3 Make a conjecture about the next item in the sequence , 12, 9, 18, 15 a. 30 c. 27 b. 45 d. 12 Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample. 38. If you have a gerbil, then you are a pet owner. a. If you are not a pet owner, then you do not have a gerbil. True b. If you do not have a gerbil, then you are not a pet owner. False; you could have a dog. c. If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets. d. If you are not a gerbil, then you are not a pet owner. True 14

15 39. line m Identify the sets of lines to which the given line is a transversal. a. lines n and o b. lines j and i c. lines i and j p d. lines j and i i and p j and p 40. In the figure, AB Ä CD. Find x and y. a. x = 29, y = 137 c. x = 137, y = 49 b. x = 41, y = 145 d. x = 49, y = 137 Determine whether '(( WX & and '( YZ & 41. W Ê Ë #2, # 5 Ê Ë # 1 Ê Ë 3 Ê ËÁ 1, 3 ˆ a. perpendicular b. neither c. parallel are parallel, perpendicular, or neither. 15

16 42. y = 2x Find the distance between the pair of parallel lines. y = 2x # 1 a. d = 1.41 c. d = 1.6 b. d = 1.34 d. d = 1.77 Identify the congruent triangles in the figure. a.!kjl %!OMN c.!klj %!ONM b.!jkl %!ONM d.!ljk %!OMN 44. Triangles ABC and AFD are vertical congruent equilateral triangles. Find x and y. a. x = 1, y = 5 c. x = 1, y = 10 b. x = 7, y = 10 d. x = 7, y = Triangle RSU is an equilateral triangle. RT bisects US. Find x and y. a. x = 4 5, y = 9 c. x = 4 5, y = 21 b. x = 4 3, y = 21 d. x = 4 3, y = 9 16

17 Identify the type of congruence transformation. 46. a. reflection or translation c. rotation or translation b. rotation only d. reflection only 47. ZC is an altitude, )CYW = 5x + 21, and )WZC = 18x. Find m)wzc. a. 54 c. 51 b. 32 d XW is an angle bisector, )YXZ = 7x + 29, )WXY = 9x # 13, and )XZY = 10x. Find m)wzx. Is XW an altitude? a. 47; yes c. 21; no b. 32; no d. 50; no 17

18 Determine the relationship between the measures of the given angles. 49. )CKT, )VTP a. )CKT < )VTP c. )CKT > )VTP b. )CKT = )VTP Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain , 7, 10 a. No; the sum of the lengths of two sides is not greater than the third. b. No; the first side is not long enough. c. Yes; the sum of the lengths of any two sides is greater than the third. d. Yes; the third side is the longest. 51. Find the measure of each interior angle for a regular nonagon. Round to the nearest tenth if necessary. a. 360 c. 40 b. 140 d Find the measure of an exterior angle of a regular polygon with 9 sides. Round to the nearest tenth if necessary. a. 40 c b. 140 d In rhombus EFGH, if EF =22, find GH. a. 11 c. 44 b. 22 d

19 54. Find the area of the figure. Round to the nearest tenth if necessary. a yd 2 c. 6 yd 2 b. 9.4 yd 2 d. 9 yd 2 Find the surface area of the cylinder. Use 3.14 for pi and round your answer to the nearest tenth. 55. a m 2 c m 2 b m 2 d m 2 Find the surface area of the regular pyramid. Round to the nearest tenth if necessary. 56. a ft 2 c ft 2 b ft 2 d ft 2 19

20 57. Suppose a spherical snowball with a diameter of 6 centimeters is melted in a large bowl. The resulting water is then poured into a cone-shaped paper cup that is 10 centimeters deep and has a diameter of 6 centimeters. The water overflows the paper cup, as the volume of the snowball turns out to be more than that of the paper cup. How much greater is the snowball s volume than that of the cone-shaped cup? Use 3.14 for \$ and round your answer to the nearest tenth. a cm 3 c cm 3 b cm 3 d. 9.2 cm Determine whether the pair of solids are similar, congruent, or neither. Figures are not necessarily drawn to scale. a. similar c. neither b. congruent d. cannot be determined Write an equation in slope-intercept form of the line having the given slope and y-intercept. 59. m: # 2 7, Ê ËÁ 0, # 2 ˆ a. y = # 2 7 x c. y = # 2 7 x # 2 b. y = 4 7 x d. y = #2x # 2 7 Write an equation in point-slope form of the line having the given slope that contains the given point. 60. m = #3, Ê ËÁ #2, 1 ˆ a. y = #3x + 3 c. y + 2 = #3(x # 1) b. y # 3 = #2(x # 1) d. y # 1 = #3(x + 2) 20

21 61. Justify the last two steps of the proof. Given: MN % PO and MO % PN Prove:!MNO %!PON Proof: 1. MN % PO 1. Given 2. MO % PN 2. Given 3. NO % ON 3.? 4.!MNO %!PON 4.? a. Symmetric Property of %; SSS c. Reflexive Property of %; SSS b. Symmetric Property of %; SAS d. Reflexive Property of %; SAS 62. State whether!abc and!aed are congruent. Justify your answer. a. yes, by SSS only b. yes, by SAS only c. yes, by either SSS or SAS d. No; there is not enough information to conclude that the triangles are congruent. 21

22 63. Can you use the SAS Postulate, the AAS Theorem, or both to prove the triangles congruent? a. AAS only c. either SAS or AAS b. SAS only d. neither 64. What additional information will allow you to prove the triangles congruent by the HL Theorem? a. )A % )E c. AC % DC b. m)bce = 90 d. AC % BD 65. Which overlapping triangles are congruent by ASA? a.!adc %!EBC c.!abe %!DEA b.!abe %!CDA d.!adc %!EDA 22

23 66. Points B, D, and F are midpoints of the sides of!ace. EC = 40 and DF = 25. Find AC. The diagram is not to scale. a. 80 b. 50 c d Find the length of the midsegment. The diagram is not to scale. a b. 58 c. 29 d DF ((( & bisects )EDG. Find the value of x. The diagram is not to scale. a. 30 b. 2 c. 5 2 d

24 69. In!ACE, G is the centroid and BE = 21. Find BG and GE. a. BG = 5 1 4, GE = c. BG = 7, GE = 14 b. BG = 14, GE = 7 d. BG = , GE = What is the orthocenter of the triangle with two altitudes given by the lines x = 1 and y = x? a. (0,2) c. none of these b. (2,2) d. (1,1) 24

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