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Name: ________________________ Accelerated Geometry Summer Assignment 5. Which angle measures approximately 72°? a. 1. The distance between points A and B is _______. b. c. 13 11 85 a. b. c. d. d. 85 2. Find the midpoint of the segment with endpoints (9, 8) and (3, 5). 3 a. (3, ) 2 b. (12, 13) 13 c. (6, ) 2 d. (1, –2) 6. If m∠IOJ = 22° and m∠HOI = 25°, then what is the measure of ∠HOJ ? 3. The nonshared sides of two adjacent angles form a pair of opposite rays. The angles are _________. a. acute b. complementary c. a linear pair d. vertical angles 4. Which one of the statements below is false? a. A circle is NOT a polygon. b. An octagon has 8 angles. c. A decagon has 10 sides. d. A pentagon has 9 angles. a. b. c. d. 1 45° 44° 52° 47° 9. A wooden fence is to be built around a 50 m-by-62 m lot. How many meters of fencing will be needed? If the wood for the fence costs $47.75 per meter, what will the wood for the fence cost? a. 3100 m, $148,025.00 b. 3100 m, $10,696.00 c. 224 m, $10,696.00 d. 224 m, $148,025.00 7. Which is not a possible value for y in the figure below? a. b. c. d. 70 115 55 160 Use the formula for the area of a triangle 1 ( A = bh) to find the value of the unknown 2 variable. 8. Which figure below is not a regular polygon? a. 10. Henry wants to use 48 feet of fencing to enclose part of his yard for a garden. Which of the figures described would use all 48 feet of fencing and enclose the largest area of Henry's yard? a. A rectangle with a length of 14 feet and a width of 10 feet b. A rectangle with a length of 16 feet and a width of 8 feet c. A square with a side length of 12 feet d. A circle with a radius of about 7.6 feet b. 11. In the figure shown, m∠AED = 124°. Which of the following statements is false? c. d. a. b. c. d. 2 ∠BEC and ∠CED are adjacent angles. ∠AEB and ∠DEC are supplementary angles. m∠AEB = 56° m∠BEC = 124° 15. In the figure, ∠6 and ∠2 are _____________. 12. Solve for x. a. b. c. d. 3 6 1 2 a. b. c. d. 13. Give the reason for the last statement in the proof. Statement Reason ∠1 and ∠2 are vertical angles. Given ∠1 ≅ ∠2 ? alternate interior angles consecutive interior angles alternate exterior angles corresponding angles ← → a. b. c. d. ← → 16. Find m∠1 in the figure below. PQ and RS are parallel. Vertical Angles Congruence Theorem Congruent Complements Theorem Congruent Supplements Theorem Linear Pair Postulate 14. In the figure, ∠1 and ∠2 are _________. a. b. c. d. a. b. c. d. 105° 75° 115° 15° 17. Which best describes the relationship between the line that passes through (7, 1) and (10, 5) and the line that passes through (–8, 5) and (–5, 9)? a. same line b. perpendicular c. neither perpendicular nor parallel d. parallel alternate exterior angles alternate interior angles consecutive interior angles corresponding angles 3 18. In the figure, l Ä n and r is a transversal. Which of the following is not necessarily true? a. b. c. d. ∠8 ≅ ∠2 ≅ ∠5 ≅ ∠7 ≅ 21. Line m is parallel to line n and they are each intersected by the same two transversals. Which angle is NOT necessarily congruent to ∠4? ∠2 ∠6 ∠3 ∠4 ← → a. b. c. d. ← → 19. In the figure shown, HC Ä GD and m∠ABC = 100°. Which of the following statements is false? a. b. c. d. ∠12 ∠16 ∠7 ∠15 22. What is the slope of the line that passes through points A (-2,-3) and B (5,3)? 6 a. 7 7 b. 6 6 c. − 7 d. 0 23. Which best describes the relationship between Line 1 and Line 2? Line 1 passes through ÊÁË −3, 6 ˆ˜¯ and ÊÁË −7, 11 ˆ˜¯ Line 2 passes through ÊÁË 1, 8 ˆ˜¯ and ÊÁË −4, 4 ˆ˜¯ a. perpendicular b. They are the same line. c. parallel d. neither perpendicular nor parallel m∠CBE = 80° m∠DEF = 80° ∠DEB and ∠CBE are corresponding angles. ∠CBE and ∠GEB are alternate interior angles. 20. Which best describes the relationship between the lines with equations −5x − 8y = 4 and − 30x − 48y = 24? a. neither parallel nor perpendicular b. same line c. parallel d. perpendicular 4 . The line that passes through 9 which of the following pairs of points is parallel to L1 ? a. (6, –3) and (2, 6) b. (12, –1) and (2, 8) c. (–5, 2) and (6, 6) d. (–3, 2) and (6, 6) 24. A line L 1 has slope 4 25. Which graph below would match the situation described? A car is traveling at 44 mph slows to 21 mph in the first 5 seconds. It maintains that speed for the next 5 seconds, and then slows to a stop in the next five seconds. a. 26. Write an equation that is parallel to y = a. b. c. d. 2 x − 7. 3 3 y = − x+7 2 2 y = x+1 3 3 y = x+2 2 2 y = − x−7 3 27. Write an equation that is perpendicular to y = −4x + 2 . a. y = 4x + 2 b. y = −4x − 2 1 c. y = x + 1 4 1 d. y = − x + 1 4 b. 28. Write an equation in slope-intercept form of the graph shown. c. a. d. b. c. d. 5 11 x−7 5 5 y= x−7 11 11 y= x−7 5 5 y =− x−7 11 y=− 29. Name a right triangle. a. b. c. d. 33. Find the value of x. ∆BDC none of these ∆ADB ∆ABC a. b. c. d. 30. A triangle has angle measures of 60°, 60°, and 60°. Choose the term that describes the triangle. a. Equiangular b. Right c. Obtuse d. Scalene 117 297 66 51 34. Find the value of x. 31. How many obtuse angles can an isosceles triangle have? a. 2 b. 3 c. 0 d. 1 a. b. c. d. 32. Find the value of x: 14° 166° 104° 28° 35. Use the figure below to solve for x. a. b. c. d. 127° 35° 88° 145° a. b. c. d. 6 55 90 145 45 36. Refer to the figure below. m∠C = a. b. c. d. 38. Which pair of lengths can be two of the sides of an isosceles triangle which has a perimeter of 52 inches? a. 15 inches, 25 inches b. 15 inches, 22 inches c. 12 inches, 22 inches d. 16 inches, 21 inches 100° 17° 148° 15° 37. The measure of ∠B is a. b. c. d. . 39. What is the value of z? (The figure may not be drawn to scale.) . 99° 89° 79° 101° a. b. c. d. z = 56 z = 25 z = 64 z = 31 40. The two triangle-shaped gardens are congruent. Find the missing side lengths and angle measures. a. b. c. d. a = 5 ft; b = 28°; c = 90°; d = 62°; e = 5 ft a = 5 ft; b = 28°; c = 62°; d = 90°; e = 5 ft a = 9.5 ft; b = 28°; c = 90°; d = 62°; e = 10.7 ft a = 5 ft; b = 28°; c = 90°; d = 62°; e = 10.7 ft 7 41. If ∆ABC ≅ ∆DEF, AB = 10 feet, m∠B = 27°, and m∠F = 14°, which of the following statements is false? a. AC = DF b. ∠C ≅ ∠F c. m∠E = 139° d. AB = DE 46. Identify the coordinates of the image point formed after (–1, 3) is reflected over the x-axis. a. (–1, 3) b. (1, 3) c. (1, –3) d. (–1, –3) 47. What is the measure of each base angle of an isosceles triangle if its vertex angle measures 40 degrees and its 2 congruent sides measure 25 units? 42. In the diagram, ∠B ≅ ∠E and ∠C ≅ ∠F . Find the value of x. a. b. c. d. x = 50 x = 25 x = 75 x = 35 a. b. c. d. 43. If ∆MNO ≅ ∆VWX, which statement is NOT true? a. NO ≅ VW b. ∠O ≅ ∠X c. MO ≅ VX d. ∠N ≅ ∠W 70° 140° 50° 40° 48. In ∆ABC , AB = 3x – 2, BC = x + 4, and AC = 7. Also AB ≅ BC . Which term does NOT describe ∆ABC ? a. Equilateral b. Acute c. Isosceles d. Obtuse 44. Given:∠B ≅ ∠E and ∠C ≅ ∠F . What other piece of information is needed to show ∆ABC ≅ ∆DEF by ASA Congruence Postulate? a. EF ≅ FE b. BC ≅ EF c. ∠A ≅ ∠D d. ∠B = ∠F 49. Given: ∆ABC ≅ ∆DEF with AB ≅ BC . Which statement of congruence is not provable? a. ∆ABC ≅ ∆CBA b. ∆DEF ≅ ∆CBA c. ∆ABC ≅ ∆FDE d. ∆ABC ≅ ∆FED 45. In ∆ABC , if AB ≅ BC and m∠A = 39°, then m∠C = . a. 102° b. 39° c. m∠B d. 141° 8 50. Given m∠NOP = m∠NPO; NO = 2n + 4; NP = 8n − 3; OP = 9; find NO. 51. What is the translation image of (–3, –6) after the translation ÊÁË x, y ˆ˜¯ → (x+ 4, y+ 3)? a. b. c. d. a. b. c. d. (–7, –9) (1, –9) (–7, –3) (1, –3) NO = 3 19 NO = 3 7 NO = 6 NO = 22 52. Refer to the figure below. Which of the following statements is true? HLK is isosceles with base HK , ∠IHL and ∠JKL are right angles, IK ≅ JH a. b. ∆HIL ≅ ∆KJL by HL ∆HLK ≅ ∆JLK by SSS c. d. ∆HKI ≅ ∆HJK by SAS There are no congruent triangles. 53. Refer to the figure shown. Which of the following statements is true? a. b. ∆TUV ≅ ∆XWV by ASA ∆TUV ≅ ∆VWX by SAS c. d. ∆TUV ≅ ∆WXV by SAS ∆TUV ≅ ∆WXV by SSS 9 56. A person facing east walks east 20 paces, turns, walks north 10 paces, turns, walks west 25 paces, turns, walks south 10 paces, turns, walks east 15 paces, and then stops. What one transformation could have produced the same final result in terms of the position of the person and the direction the person faces? a. reflection over the north-south axis b. rotation c. translation d. reflection over the east-west axis 54. Identify the coordinates of the point (–5, –3) after a rotation of 180° clockwise about the origin. a. (–5, 3) b. (5, 3) c. (–3, –5) d. (5, –3) 55. Which graph represents a reflection in the x -axis? a. 57. A right triangle is placed in a convenient position in the first quadrant of a coordinate plane. Which is the missing label for the vertex? b. a. b. c. d. c. ÊÁ v,0 ˆ˜ Ë ¯ (0,u) (0,v) ÊÁ u,v ˆ˜ Ë ¯ 58. For the triangle shown, VS = 5 and VQ = 6. Then PQ = ______. d. a. b. c. d. 10 11 12 10 5 → 5 x + 4 and AE = 6x + 4. 2 Assume B is the midpoint of AC and D is the midpoint of CE. 61. OE bisects ∠BOA, EA ⊥ OA, and EB ⊥ OB. Which statement is NOT true? 59. Solve for x given BD = a. b. c. d. a. − b. c. 4 2 d. − 1 2 AE ≅ BE ∠AOE ≅ ∠EAO OA ≅ OB ∠AEO ≅ ∠BEO a c = , then ______. b d a+b c+b = a. b d b. ac = bd a+b c+d c. = b d a a+c d. = b b+d 62. If 1 4 ← → 60. Given: BC is the perpendicular bisector of KM . Which statement is true? 1 inch : 28 miles. If the 2 actual distance between the two cities is 448 miles, how far apart are they on the map? a. 16 inches b. 32 inches c. 8 inches d. 4 inches 63. A map has a scale of a. ∠BLM, ∠MLC , ∠CLK, ∠KLB b. c. d. are all right angles. CM = BM ∠KBM is a right angle. C is the midpoint of KM 11 67. If two polygons are SIMILAR, then the corresponding sides must be _____. a. proportional b. congruent c. parallel d. similar 64. The Community Recreation Center is developing plans for a new sports facility. Community members can submit suggestions for the new facility, along with basic scale drawings of their ideas. Rachel wants to include a new 11- by 24-meter tennis court in the athletic center. She is submitting a scale drawing on an 8.5- by 11-inch sheet of paper. Which scale should Rachel use to create as large a drawing as possible on the paper? 3 in. = 1 m a. 8 3 b. in. = 1 m 4 1 c. in. = 1 m 8 7 d. in. = 1 m 16 68. Given that ∆ABC ∼ ∆DEF, solve for x and y. 65. Are the two polygons similar? (They are not drawn to scale, but assume all angles are 90°.) If not, explain why. a. b. c. d. x = 9.75, y = 11.2 x = 8.75, y = 11.2 x = 8.75, y = 10.2 x = 9.75, y = 10.2 69. The perimeter of ∆PQR is 80, PQ = 30, ∆PQR ∼∆STU, and ST = 18. What is the perimeter of ∆STU? a. 18.4 b. 6.8 c. 48 d. 24 a. b. c. d. 70. A rectangle has a length of 9 mm. A similar rectangle is drawn using a scale of 1:3. What is the length of the second rectangle? a. 9 mm b. 6 mm c. 3 mm d. 4 mm Yes 5 6 ≠ 25 10 not enough information to tell 5 8 No; ≠ 25 41 No; 66. If two polygons are SIMILAR, then the corresponding angles must be _____. a. complementary b. supplementary c. congruent d. linear pairs 12 73. Two ladders are leaning against a wall at the same angle as shown. 71. The triangles below are similar. Find x. a. b. c. d. 2.9 130 123.5 49.4 72. Which triangle is NOT similar to any of the others? How far up the wall does the shorter ladder reach? a. 16 ft b. 18 ft c. 22 ft d. 36 ft a. b. 74. One way to show that two triangles are similar is to show that ______. a. two angles of one are congruent to two angles of the other b. two sides of one are proportional to two sides of the other c. a side of one is congruent to a side of the other d. an angle of one is congruent to an angle of the other c. d. 75. The postulate or theorem that can be used to prove that the two triangles are similar is _____. a. b. c. d. 13 SAS Similarity Theorem ASA Congruence Theorem SSS Similarity Theorem AA Similarity Postulate 79. For the figure shown, which statement is not true? 76. If the corresponding sides of two triangles are proportional, then _____. a. the triangles are right triangles b. the triangles are similar c. corresponding side lengths are equal d. the triangles are congruent 77. Given: PQ || BC . Find the length of AQ. a. b. c. d. w x = y z wx = yz wz = xy w y = x z 80. The dashed triangle is the image of the solid triangle for a dilation with center at the origin. What is the scale factor? a. b. c. d. 17 19 12 15 78. If ∆ABC ~ ∆PBQ, then which of the following proportions is NOT true? a. b. a. b. c. d. AC CB = PQ QB AP AC = PB PQ AP CQ = PB QB PB PQ = AB AC c. d. 14 2 3 3 2 3 1 3 81. One triangle is shown on the coordinate grid. Two vertices for a second triangle are also shown. Which coordinates for the third vertex will form another triangle that is similar to the triangle that is shown? a. b. c. d. ÊÁ −7, Ë ÊÁ −7, Ë ÊÁ −7, Ë ÁÊ −7, Ë In the figure below, ∆ABC ∼ ∆A' B ' C ' . 82. Which statement is true of the transformation from ∆ABC to ∆A' B ' C ' .? a. The measures of all corresponding angles change by a scale factor of 2. b. The measures of all corresponding angles 1 change by a scale factor of . 2 c. The lengths of all corresponding sides change by a scale factor of 2. d. The lengths of all corresponding sides change 1 by a scale factor of . 2 − 7 ˆ˜¯ − 2 ˆ˜¯ − 5 ˆ˜¯ 5 ˆ˜¯ 83. For the triangle shown below, the Pythagorean Theorem states that _____. a. b. c. d. 15 e2 + f 2 = g2 e=f+g f 2 − g2 = e2 e2 = f 2 + g2 84. If a, b, and c are sides of a right triangle, which of the following are also sides of a right triangle? a. The square root of each length ( a , b , b. c. d. 88. A freshly-planted sapling is braced by 3 cables attached to a collar secured to the sapling 8 feet up the trunk. Each cable is staked into the ground 3 feet from the sapling's trunk. c) Twice the length of each side (2a, 2b, 2c) Four more than each length (a + 4, b + 4, c + 4) The square of each length 85. Which of the following sets of numbers is a Pythagorean triple? a. 3, 4, 5 b. 12, 16, 20 1 1 1 c. , , 3 4 5 d. 3 2 , 4 2 , 5 2 86. A set of Pythagorean triples is _____. a. 3, 5, 9 b. 1, 1, 2 c. 6, 9, 12 d. 5, 12, 13 If fastening a cable to the collar uses 8 inches of cable and fastening it to its stake also uses 8 inches of cable, about how much cable has been used? 87. A 25.5 foot ladder rests against the side of a house at a point 24.1 feet above the ground. The foot of the ladder is x feet from the house. Find the value of x to one decimal place. a. b. c. d. about 29.6 feet about 27.6 feet about 25.3 feet about 26.3 feet 89. Which set of lengths cannot form a right triangle? a. 6 mm, 12 mm, 13 mm b. 5 mm, 12 mm, 13 mm c. 2.5 mm, 6 mm, 6.5 mm d. 10 mm, 24 mm, 26 mm a. b. c. d. 90. If the side lengths of a triangle are 7, 6, and 9, the triangle _____. a. is an obtuse triangle b. is a right triangle c. is an acute triangle d. cannot be formed 1.9 7.0 8.3 10.1 91. Choose the set that is the possible side lengths of a right triangle. a. 1, 1, 2 b. 1, 1, 2 c. 3, 4, 7 d. 3, 5, 9 16 95. An equilateral triangle has side lengths of 10. The length of its altitude is _____. a. 10 5 b. 5 c. 5 10 92. A board 8 feet long is to be used as a temporary brace for a section of fence that has a broken post. If the board is nailed to the fence 6 feet above ground level, about how far from the base of the fence is the other end of the board when it is fastened to a stake in the ground? d. 5 3 96. The tangent of ∠B is _____. a. b. c. d. 95 7 95 12 7 95 12 7 97. The cosine of ∠A is the ratio _____. a. b. c. d. 7.2 feet 5.3 feet 6.8 feet 2 feet 93. Choose the set that is the possible side lengths of a right triangle. a. 4, 9, 13 b. 2, 2, 2 c. 1, 1, 2 d. 8, 15, 25 a. b. 94. Which of the following cannot be the lengths of a 30°-60°-90° triangle? 21 42 21 a. , , 3 13 13 13 b. 23, 46, 46 3 c. d. c. d. 27, 54, 27 3 6, 12, 6 3 17 adj. hyp. opp. hyp. hyp. adj. opp. adj. 102. Find tan B for the right triangle below: 98. To find the height of a tower, a surveyor positions a transit that is 2 meters tall at a spot 95 meters from the base of the tower. She measures the angle of elevation to the top of the tower to be 32°. What is the height of the tower, to the nearest meter? a. 154 m b. 59 m c. 61 m d. 152 m 99. A slide 4.1 m long makes an angle of 27° with the ground. How high is the top of the slide above the ground? a. 1.86 m b. 3.65 m c. 1.93 m d. 2.09 m a. b. c. d. 100. Which statement is true? a. All quadrilaterals are squares. b. All rectangles are squares. c. All parallelograms are quadrilaterals. d. All quadrilaterals are parallelograms. 8 17 15 17 8 15 15 8 103. Find x. Round the result to the nearest hundredth. 101. What is x to the nearest hundredth? (not drawn to scale) a. b. c. d. a. b. c. d. x = 13.51 x = 11.15 x = 10.04 x = 16.66 104. Which of the following is NOT enough information to solve a right triangle? a. Two sides b. One side length and one trigonometric ratio c. Two angles d. One side length and one acute angle measure x = 16.66 x = 13.51 x = 11.15 x = 10.04 105. Find the measure of each exterior angle of a regular polygon with 16 sides. a. 11.25° b. 360° c. 22.5° d. 157.5° 18 106. Choose the statement that is NOT ALWAYS true. For any parallelogram _______. a. the diagonals bisect each other b. opposite angles are congruent c. the diagonals are perpendicular d. opposite sides are congruent 111. Identify two chords. 107. If ON = 7x − 5, LM = 6x + 3, NM = x − 4, and OL = 2y + 5, find the values of x and y given that LMNO is a parallelogram. a. b. c. d. a. b. c. d. IJ and KL GH and KL GH and IJ GI and HJ 112. A circle is the set of all points in a plane that _____. a. have a center b. are equidistant from a given point c. have a diameter d. lie within a given radius 1 13 ;y= 2 2 x = 8; y = −2 1 x = 8; y = − 2 x = 2; y = −2 x= 113. A segment with endpoints on a circle is a _____. a. secant b. radius c. tangent d. chord 108. Choose the statement that is NOT ALWAYS true. For a rhombus ________. a. each diagonal bisects a pair of opposite angles b. all four sides are congruent c. the diagonals are congruent d. the diagonals are perpendicular 114. The center of a circle lies on _____. a. every diameter b. the circle c. a tangent line d. every chord 109. The diagonals of a parallelogram always _________. a. are congruent b. are parallel c. bisect each other d. are perpendicular 115. If a circle has a diameter of 12, then it has _____. a. a radius of 4 b. a radius of 24 c. a radius of 6 d. a diameter of 6 110. Which statement is NOT always true of a rhombus? a. The diagonals are perpendicular to each other. b. The diagonals bisect each other. c. Each diagonal is longer than at least one side. d. The sum of the diagonals is less than the perimeter. 116. A line which intersects a circle at exactly one point is called_____. a. a point of tangency b. a tangent line c. a chord d. a secant 19 120. A wooden wagon wheel has 12 equally spaced spokes radiating from the central hub. 117. The circle is circumscribed by the pentagon as shown (not drawn to scale). If QZ = 10, YX = 9, XW = 13, UW = 16, and SU = 17, find the perimeter of the pentagon. a. b. c. d. What is the measure of the angle that determines the separation between two adjacent spoke holes? a. 22.5° b. 30° c. 12° d. 45° 120 98 130 88 121. Find the value of x. 118. Use the figure. SR is tangent to ñQ at R. Choose the true statement. a. m∠RQS + m∠QSR = 180° b. m∠RQS = 90° c. m∠SRQ = 90° d. SQ ≅ SR 119. RP is tangent to ñG at P. RQ is tangent to ñG at Q. Choose the statement that is NOT true. a. b. c. d. a. b. c. d. ∠GRP ≅ ∠GRQ ∠PGR ≅ ∠QGR PR ≅ QR ∠GPR is obtuse. 20 11.6 12.4 6.7 8.0 126. If the sides of a square are made eight times longer, how many times the area of the original figure is the area of the new figure? a. 128 times b. 8 times c. 64 times d. 640 times 122. Given AC bisects BD , choose the true statement that refers to the figure. a. CD = BA b. c. BCD is a major arc. AC is a diameter. d. BAD is a minor arc. 127. For a circle of radius 5 feet, find the length of an arc s with a measure of 28°. 7 a. s = π feet 9 7 b. s = π feet 18 1 c. s = π feet 36 d. s = 140π feet 123. Write the standard equation of a circle with its center at the origin and radius 3. a. x 2 + y 2 = 6 128. Find the length of a 40° arc in a circle with a radius of 4. 8π a. 9 b. 8π 9π c. 8 16π d. 9 2 b. c. d. y x2 + =1 6 6 x2 + y2 = 9 x2 + y2 = 3 124. A rectangle has length l and width w. An expression for its area is _____. a. 2(l + w) b. c. d. 2 l +w l⋅w lw 129. In this figure, each circle has a radius of 2 inches. What is the area of the portion outside the circles but inside the square? Express your answer in terms of π. 2 125. The area of the parallelogram is _____. a. b. 680 sq. units 800 sq. units c. d. 40 111 sq. units 340 sq. units a. b. c. d. 21 24 − 8π 24 − 12π 144 − 4π 144 − 36π 130. A survey about the student government program at the school found that 350 students wanted after-school student government programs, 210 students wanted student government classes during the day, and 140 students thought that the school should have no student government program. If a circle graph were made from this data, what would be the measure of the central angle for the "in-school" group? a. 110° b. 108° c. 210° d. 205° 134. Find the exact volume of a cylinder that has a height of 18 inches and a radius of 8 inches. a. 384π in 3 b. 288π in 3 c. 1152π in 3 d. 144π in 3 135. Find the volume of the right triangular prism. 131. Find the area of the shaded region. a. b. c. d. a. b. c. d. 153.94 cm2 30.79 cm2 123.15 cm2 38.48 cm2 210 m3 31 m3 105 m3 20.5 m3 136. A cylindrical vase has a diameter of 4 inches and a height of 14 inches. You place some marbles at the bottom of the vase that take up about 38 cubic inches. You fill vase with water up to 3 inches from the top. Write an expression you can use to determine the approximate volume of water in the vase? 2 a. π (4) (14) − 38 132. Find the area of an equilateral triangle with side length 14. a. 21 3 b. 42 c. 98 d. 49 3 b. 133. An aquarium in a restaurant is a rectangular prism and measures 4.5 feet by 4 feet by 2 feet. What is the volume of the aquarium? a. 32 cubic feet b. 36 cubic feet c. 10.5 cubic feet d. 12.5 cubic feet c. d. 22 2 π (4) (14 − 3) − 38 2 π (2) (14 − 3) − 38 2 2 π (2) (14) − 3 (2) − 38 139. Find the volume of a sphere 4 ft in diameter. Use π ≈ 3.14 and round your answer to the nearest tenth. a. 16.7 ft 3 b. 18.8 ft 3 c. 33.5 ft 3 d. 25.1 ft 3 137. The pyramid shown has a rectangular base and faces that are isosceles triangles. Find its volume. 140. What is the volume of a sphere with diameter 9.4 feet? a. 434.9 ft 3 b. 277.6 ft 3 c. 69.4 ft 3 d. 92.5 ft 3 a. b. c. d. 80 ft 3 240 ft 3 34 ft 3 384 ft 3 Simplify: 141. 300 a. 10 30 b. 10 3 c. 30 d. 3 10 142. 200 a. 10 b. 5 c. 50 d. 20 138. A pyramid-shaped puzzle exactly fits its cubic storage box. The space between the puzzle and the sides of the box is filled with a light-weight plastic foam to help protect the puzzle during shipping. 2 2 2 2 Simplify: 143. 10 ⋅ 4 a. 2 10 b. 4 5 c. 2 5 d. 40 144. 30· a. 9 b. 12 c. 6 d. 3 What is the volume of the foam? a. 171.50 cm3 b. 228.67 cm3 c. 240.10 cm3 d. 114.33 cm3 23 12 20 10 10 40 145. 11 a. b. c. d. 25 137.5 16 55 27.5 Simplify: 146. a. b. c. d. 49 100 7 50 3 4 7 100 7 10 147. Topics that you should know from Acc Alg include, but are not limited to: 1) Angles with parallel lines and transversals 2) Triangle Congruences andSimiliarities 3) Properties of Quadrilaterals 4) Properties of Circles 5) Volume of solids 6) Triangle and Angle Proofs 7) Special Right Triangles 8) Right Triangle Trigonometry 9) Pythagorean Theorem 10) Triangle Midsegment 11) Distance and Midpoint Formulas 12) Area and Perimter Formulas 13) Slope and Parallel and Perpendicular Lines 148. This assignment will be due the first week of school.There will be a test over this material within the first week of school. This material also covers half of the material on the Geometry Milestones test you will take in December. Good luck and work hard ! 24 ID: A Accelerated Geometry Summer Assignment Answer Section 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. C C C D D D C D C C B A A A D A D D C B B A A D D B C A D A D D D A D B D B C D C B 1 ID: A 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. A B B D A D C B D A C B B C C C B A B C C D D C A B C C C D B A D B D B B D C D D B B D C 2 ID: A 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. A A C B B B B D A A C A C D D C C C C C C C C C B D A C B B C D B C C C C A C A A D B B D 3 ID: A 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. B C C C A B C A B A A C C D b d 4