Geometry Cumulative Review
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1 Geometry Cumulative Review Name 1. Find a pattern for the sequence. Use the pattern to show the next term. 1, 3, 9, 27,... A. 81 B. 45 C. 41 D If EG = 42, find the value of y. A. 5 B. C. 6 D. 7 E 3y 4 F y 2 G 3. Find a pattern for the sequence. Use the pattern to show the next term. S, M, T, W,... A. S B. H C. M D. T Use the figure at the right for Exercises What is the intersection of plane GHIJ and plane CDIH? A. B. point H C. D. 5. Which four points are coplanar? A. A, B, E, I B. B, C, D, E C. A, C, F, H D. E, F, I, K 6. What is another way to name plane ABEF? A. point A B. C. plane ACDF D. plane CDIH 7. What is the intersection of and plane ACHG? A. B. point E C. D. point B 8. Find the value of x. A. 3 B. 4 C. 5 D is the of LON. A. perpendicular bisector B. midpoint C. segment bisector D. angle bisector 10. Which figures in the third group are widgets? A. I and III B. I and IV C. I, III, and IV D. I, II, and IV 11. Find the value of x. A. 35 B. 45 C. 90 D Which property of equality or congruence justifies the following? A. Reflexive Property B. Symmetric Property C. Transitive Property D. Distributive Property Can you make each conclusion from the information in the diagram? Explain
2 Complete with always, sometimes, or never to make each statement true. 16. The intersection of two distinct planes is one line. 17. The sum of the measures of two complementary angles is Find the coordinates of points C and D. 19. Find the coordinates of the midpoint of 20. Find the length of If something is a bird, then it can fly. 21. hypothesis a. it can fly 22. conclusion b. something is a bird 23. Which is a counterexample of this conditional? A. sparrow B. cardinal C. ostrich D. crow 24. In the diagram at the right, what is the measure of 1? A. 60 B. 120 C. 30 D What is the length of with endpoints at A(5, -1) and B(2, 3)? A. 5 B. 7 C. 9 D Deshonda is selling granola bars to support her school band. On Monday she sells 16 bars, on Tuesday she sells 8 bars, and on Wednesday she sells 4 bars. If the pattern continues, how many bars will she sell on Thursday? A. 0 B. 1 C. 2 D If WZ = 46, find the value of y. A. B. 7 C. 8 D Which can be the intersection of two distinct lines? A. point B. line C. plane D. ray 29. Refer to the diagram at the right. Which segment is not parallel to A. B. C. D. 30. What is the value of x? A. 9 B. -10 C. 11 D Find the next two terms of the sequence. 10, -14, 18, A. -26, 30 B. -30, 26 C. 26, 30 D. 26, -30 B. 32. Which equation follows from 3 by the Addition Property of Equality? A. 4 2 B. 4 C. 4 D. 33. Refer to the diagram at the right. If find the value of s. 34. Write the converse of the following statement, and decide whether is true or false. If a polygon is a triangle, then it has three sides.
3 35. Find the area of a circle with a circumference of 28π m. 36. Why is the following statement not a good definition? A linear pair is two angles whose sum is What is the intersection of plane ABF and plane BDG? 38. What property justifies the following? Find the coordinates of the center of a circle with diameter. 39. Q(2, 1), R(-4, 3) 40. Q(-5, -1), R(1, 5) 41. What is the length of the segment with endpoints M(2, -1) and N(-6, 8)? 42. Find x if the perimeter of rectangle ABCD is 22. For the given dimensions, find the area of each figure to the nearest hundredth. 43. Rectangle: b = 10 m and h = 6 m 44. Circle: d = 22 cm 45. Which line is parallel to? A. 4 2 B. 4 C. D. 46. Classify the triangle at the right by its sides. A. isosceles triangle B. scalene triangle C. equilateral triangle D. right triangle Exercises 46, Find the value of x. A. 40 B. 30 C. 20 D Which line is perpendicular to 2? A B. 2 4 C. 3 2 D Classify 2 and 4 in the figure at the right. A. alternate interior angles B. alternate exterior angles C. same-side interior angles D. corresponding angles 50. Find the value of x in the figure at the right. A. 10 B C. 20 D Find the diameter of a circle with a radius of 4. A. B. 4 2 C. 4 3 D. 2
4 52. What is the midpoint of the segment with endpoints (2, 8) and (-6, 10)? A. (-2, 9) B. (-4, 1) C. (-4, 9) D. (-2, 1) 53. Classify the figure by its sides. A. triangle B. hexagon C. pentagon D. quadrilateral 54. What is the classification of a triangle with one angle greater than 90? A. scalene triangle B. acute triangle C. right triangle D. obtuse triangle B. 55. What is the circumference of a circle with an area of 64π in. 2? A. 8π in B. 32π in C. 64π in D. 16π in 56. What is the slope of a line parallel to if A(4, -3) and B(-1, 7)? A. 2 B. -2 C. D. 57. Which property of equality or congruence justifies the following statement? 3 3 A. Subtraction B. Division C. Reflexive D. Transitive 58. Find the distance between S(-1, 3) and T(4, -9) A. 5 B. 12 C. 13 D What is the area of rectangle LMNO? A. 7 B. 364 C. 26 D What is the perimeter of rectangle LMNO? A. 28 B. 56 C. 80 D. 160 Supply the reason for each step in the proof. Given: Prove: = = = Is it possible to have a scalene isosceles triangle? Explain. 67. Find the value of x. A. 110 B. 70 C. 45 D Why is ΔLMP ΔOMN? A. ASA B. SAS C. AAS D. SSS B. 69. What is the intersection of and plane FAC? A. B. C. plane FAC D. point B
5 70. What can you conclude from the diagram? A. ΔABC ΔADB B. C. ΔABD is isosceles D. BD = Pentagon LMNOP TQRSV. Which segment is congruent to A. B. C. D. 72. What is the measure of x? A. 66 B. 132 C. 48 D Which is true about all right triangles? A. Two sides are congruent. B. They have two acute angles. C. They have one obtuse angle. D. They have a second right triangle. 74. What is? A. 5 B. 65 C. 45 D If the midpoint of is (4, 3) and point A has coordinates (-2, 6), what are the coordinates of point B? A. (1, 4.5) B. (10, 0) C. (3, 1.5) D. (2, 9) 76. Find the value of x. A. 45 B. 35 C. 30 D Which condition will prove that? A. 1 3 B. 7 6 C. m 4 + m 8 =180 D Find the measure of x and y. 79. The reasons in this proof are listed in the wrong order. Rewrite them in the correct order. Given: Prove: Statements Reasons 1. a. Reflexive Property 2. b. SAS Theorem 3. c. Given 4. d. CPCTC Theorem 5. e. Given 80. What conditions do not prove two triangles are congruent? 81. At the local bakery a small chocolate chip cookie has a diameter of 2 in. How much more cookie do you get if you buy a supercookie with a diameter of 6 in.? A. 8 in. 2 B. 10 in. 2 C. 32 in. 2 D. 40 in Find the value of x in the diagram at the right. A. 5.5 B. 11 C. 22 D Which side lengths would not make a triangle? A. 2, 4, 5 B. 3, 8, 6 C. 4, 5.1, 9 D. 4, 3, 7
6 84. Find the value of y in the diagram at the right. A. B. C. 3 D The lengths of the sides of ABC are AB = 8, BC = 6, and AC = 10. Put the angles in order from smallest to largest. A. A, B, C B. A, C, B C. B, C, A D. B, A, C 86. What can you conclude about the diagram at the right? A. LNO is isosceles. B. is a midsegment C. LMP LPM D. 87. What is the next number in the sequence? 128, 64, 32, 16, 8,... A. 5 B. 10 C. 15 D Which is not a point of concurrency? A. centroid B. orthocenter C. median D. incenter 89. Which are the appropriate names for the polygon shown at the right? I. quadrilateral II. rectangle III. parallelogram IV. rhombus A. I and IV B. I and II C. III and IV D. I and III 90. Which line is perpendicular to? A. 3 B. 4 2 C. 3 D What is the inverse of the statement If the sky is blue, then it is not raining? A. If the sky is not blue, then it is raining. B. If it is not raining, then the sky is blue. C. If it is raining, then the sky is not blue. D. If the sky is blue, then it is raining. 92. Find m 1 in the diagram at the right. A. 50 B. 55 C. 60 D Complete the statement: In LMN, LM + LN A. < LN B. > MN C. = LN D. > LN + LM 94. If LN = 42, find LM. 95. Find AC. 96. Find the coordinates of the center of a circle with diameter so that Q(2, 1) and R( --4, 3). 97. Find the value of x in parallelogram ABCD. A. 1 B. 2 C. 3 D Find the value of x in parallelogram WXYZ. A. 70 B. 75 C. 105 D. 110
7 99. The measure of BIR equals which of the following? I. m DBI II. 2m DBI III. A. I only B. I and II C. I and III D. II and III 100. The measure of an angle is six more than twice the measure of it supplement. Find the measure of the angle. A. 58 B. 62 C. 118 D Find the perimeter of ABC at the right. A. 28 B. 14 C. 22 D Which angle is congruent to CAB? A. NLM B. LNM C. LMN D. MNL 103. An isosceles triangle has two angles measuring 55 and 70. What is the measure of the third angle? A. 70 B. 55 C. 15 D Which conditions are sufficient to prove that a quadrilateral is a square? I. All four sides are congruent. II. The diagonals are congruent. III. The diagonals bisect each other. A. I only B. I and II C. I and III D. II and III 105. What is in the triangle at the right? A. a perpendicular bisector B. a median C. an altitude D. an angle bisector 106. Which line is parallel to 3? A. 3 4 B. 2 4 C. 2 4 D The lengths of two sides of a triangle are 4 yd and 8 yd. Which of the following cannot be the length of the third side? A. 3 yd B. 5 yd C. 8 yd D. 9 yd 108. Determine the value of y for which in the diagram at the right A triangle has angle measures of 2x + 8, 3x +5, and 6x + 2. What is the measure of each angle from smallest to largest? 110. Find XW. A. 4 B. C. D What can you conclude from the diagram? A. Y Z B. XYW ZYX C. XWY XWZ D. none of the above 112. Find the value of x. A. 18 B. 3.6 C. 44 D Points T and P lie on circle C. CT = 10 and m PCT = 90. Find the length of A in. B. 5 in. C. 10 in. D. 20 in.
8 114. Lines l 1 and l 2 intersect to form congruent supplementary angles. What can you conclude? A. Lines l 1 and l 2 are skew. B. Lines l 1 and l 2 are parallel. C. Lines l 1 and l 2 are perpendicular. D. None of the above RSTU is a rectangle. Find RP. A. 13 B. 8.5 C. 6.5 D. cannot be determined from the given information 116. Find m B. A. 50 B. 80 C. 71 D What can you conclude form the diagram? A. m P < m N B. m N < 65 C. m P < 65 D. NK < NP 118. Refer to the triangle at the right to find the value of x. A. 8 B. C. D Refer to the triangle at the right to find the value of y. A. B. 12 C. 15 D Refer to the figure at the right to find the value of a. A. 7 B. 21 C. 84 D Which quadrilateral must have perpendicular diagonals? A. parallelogram B. rectangle C. rhombus D. isosceles trapezoid 122. The diagonals of which quadrilateral bisect each other? A. parallelogram B. rectangle C. rhombus D. all of the above 123. KMP is isosceles with KM = KP. and are angle bisectors. What can you conclude? A. KMP is isosceles. B. and are medians. C. and are altitudes. D. none of the above Refer to the triangle at the right to find the measure of QR State the contrapositive of the statement If pigs can fly, then cows have six legs Find the value of x to the nearest tenth. A B. 7.0 C. 3.9 D By which postulate or theorem are the triangles congruent? A. HL B. SAS C. SSS D. AAS
9 128. What is the exact length of x? A B. 5 3 C D TQR MNO. Find ON and TQ. A. 3.75, 2.4 B. 2.4, 5 C. 16, 3.2 D. 3.75, The hypotenuse of an isosceles right triangle is 6 ft long. What is the length of one leg? A. 6 2 B. 3 2 C. 12 D A triangle has angle measures of What are the measures of the angles from the smallest to largest? A. 30, 58, 92 B. 33, 47, 100 C. 38, 50, 92 D. 38, 52, Which is the greatest in ABC? A. sin A B. cos C C. tan A D. tan C 133. A right triangle has a leg that is 5 in. long and a hypotenuse that is 13 in. long. Find the length of the third side. A. 6 in. B. 8 in. C. 10 in. D. 12 in A 15-ft ladder slides down a wall of a building until the ladder forms a 52 angle with the ground. How high up the wall will the ladder reach at this point? A ft B ft C. 19 ft D ft B A stone pathway forms the diagonal of a square garden. One side of the garden is 40 ft. How long is the pathway? A. 40 ft B. 4 2 ft C. 4 3 ft D. 80 ft 136. Find the length of segment AB with endpoints at A(-4, 6) and B(-1, 2). A. 8 B. 2.6 C. 11 D Which quadrilateral has congruent diagonals? A. trapezoid B. parallelogram C. rhombus D. rectangle 138. Find the value of x in the figure at the right Find the value of x in the figure at the right. A. 10 B C. 20 D Which line is perpendicular to 2 A. 2 3 B. 3 2 C. 2 3 D Find the measure of in K. A. 110 B. 145 C. 160 D Find the volume of a sphere with radius 6 m. A. 48 m 3 B. 144 m 3 C. 168 m 3 D. 288 m 3
10 143. What is the diameter of a circle with radius 4 3 A. 2 3 B. 4 3 C. 3 D Find the midpoint of with A(4, 3) and B(6, -5). A. (10, 2) B. (5, 4) C. (10, -2) D. (5, -1) 145. What is the area of a triangle whose longest side has length 14 cm? Round your answer to the nearest whole number State the inverse of the following statement: If a triangle is right, then the Pythagorean Theorem can be applied To the nearest hundredth, what is the value of x in the equation, 4? 148. At the local pizzeria, a small pizza has an 8-in. diameter. How much more pizza do you get if you buy a large pizza with a diameter of 16 in.? A. 2 in 2 B. 48 in 2 C. in 2 D. in Find the value of x. A. 23 cm B cm C. 2 3 cm D. 4 2 cm 150. A right triangle has a leg that is 5 in. long and hypotenuse that is 13 in. long. Find the length of the third side. A. 6 in. B. 8 in. C. 10 in. D. 12 in Find the value of y. A. B. C. 3 D Find the length of segment AB with coordinates A(-4, 6) and B(-1, 2). A. 8 B. 2.6 C. 11 D Find the length of A. yd B. 4 yd C. 4 yd D. yd 154. Find the area of a square with radius 5 cm. A. 25 cm 2 B. 50 cm 2 C m 2 D. 100 cm Find m 1. A. 38 B. 62 C. 68 D Which quadrilaterals always have both pairs of opposite sides congruent? I. a trapezoid II. a parallelogram III. a kite A. II only B. II and III C. I and II D. I and III 157. Find the total area of the shaded regions. A. (32-16 ) cm 2 B. (16-32) cm 2 C. (64-32 ) cm 2 D. (32-64) cm If LN = 42, find LM. A. 24 B. 18 C. 8 D. 6
11 159. Find AC. A. 4 B. 8 C. 14 D Find the area of a regular pentagon that measures 6 m on a side and has an apothem 4.1 m long Find the surface area of the right rectangular prism. A. 83 m 2 B. 140 m 2 C. 146 m 2 D. 166 m Find the lateral area of the cylinder. A. 4 ft 2 B. 6 ft 2 C. 4 ft 2 D. 8 ft The measure of an angle is 3 more than twice the measure of its supplement. Find the measure of the angle. A. 59 B. 63 C. 117 D Which of the following are not Pythagorean Triples? I. 3, 4, 6 II. 5, 12, 13 III. 8, 15, 16 IV. 7, 24, 25 A. I only B. I and II C. I and III D. I, III, and IV 165. A rhombus has a 60 angle and sides 6 cm long. What is its area? A. 18 cm 2 B cm 2 C. 36 cm 2 D cm Find the lateral area of the regular square pyramid at the right. A. 84 cm 2 B. 96 cm 2 C. 12 cm 2 D. 48 cm The cone-shaped funnel has height 9 cm and a rim with circumference 12 cm. What is the volume of the funnel? A. 54 cm 2 B. 108 cm 2 C. 162 cm 2 D. 324 cm What is? A. a perpendicular bisector B. a median C. an altitude D. an angle bisector 169. Find the area of regular decagon with an apothem of 4 cm.. A. 24 cm 2 B. 26 cm 2 C. 180 cm 2 D. 240 cm Find the volume of the sphere. A ft 3 B ft 3 C. 768 ft 3 D. 576 ft Find the value of x in the figure at the right. A. 57 B. 64 C. 63 D The lengths of two sides of a triangle are 4 yd and 8 yd. Between what two lengths must the third side measure? 173. Find the value of x. A. 2 B. 2 2 C. 4 2 D. cannot be determined from the information given PQRS is a parallelogram. What can you conclude? A. PQ = RQ B. m P = m S C. D.
12 175. Find the value of x. A. 10 B. 9 C. 8 D Find the value of w. A. 1 B. C. 2 D Find the value of y. A. 12 B. C. 4 D Find the value of x. A. 40 B C. 10 D. Cannot be determined from the information given 179. Which quadrilateral must have congruent diagonals? A. rectangle B. rhombus C. trapezoid D. parallelogram 180. Find the value of x. A. 130 B. 50 C. 30 D. Cannot be determined from the information given Find the value of y. A. 50 B. 100 C. 110 D A pentagon contains two right angles and two 120 angles. Find the measure of the remaining angle. A. 108 B. 90 C. 120 D Find the total surface area of a cylinder with height 4 cm and radius 3 cm. A. 33 cm 2 B. 40 cm 2 C. 42 cm 2 D. 56 cm What is the area of a triangle whose longest side has length 12 cm? A. 72 cm 2 B cm 2 C cm 2 D cm Find the length of the segment whose endpoints are (2, -3) and (-6, 2) 186. State the converse of the statement If a triangle is acute, then it is not a right triangle Find the measure of each interior angle in a regular octagon.
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