Accelerated Geometry Summer Assignment

Transcription

1 Name: Accelerated Geometry Summer Assignment 1. The distance between points A and B is. 5. Which angle measures approximately 72? b. c. 13 b. 11 c Find the midpoint of the segment with endpoints (9, 8) and (3, 5). (3, 3 2 ) b. (12, 13) c. (6, 13 2 ) (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. acute b. complementary c. a linear pair vertical angles 4. Which one of the statements below is false? A circle is NOT a polygon. b. An octagon has 8 angles. c. A decagon has 10 sides. A pentagon has 9 angles. 45 b. 44 c

2 7. Which is not a possible value for y in the figure below? 70 b. 115 c Which figure below is not a regular polygon? b. c. 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? 3100 m, $148, b m, $10, c. 224 m, $10, m, $148, Use the formula for the area of a triangle (A = 1 bh) to find the value of the unknown 2 variable. 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 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 A circle with a radius of about 7.6 feet 11. In the figure shown, m AED = 124. Which of the following statements is false? BEC and CED are adjacent angles. b. AEB and DEC are supplementary angles. c. m AEB = 56 m BEC = 124 2

3 12. Solve for x. 15. In the figure, 6 and 2 are. 3 b. 6 c Give the reason for the last statement in the proof. Statement 1 and 2 are vertical angles. 1 2? Reason Given Vertical Angles Congruence Theorem b. Congruent Complements Theorem c. Congruent Supplements Theorem Linear Pair Postulate alternate interior angles b. consecutive interior angles c. alternate exterior angles corresponding angles 16. Find m 1 in the figure below. PQ parallel. and RS are 14. In the figure, 1 and 2 are. 105 b. 75 c alternate exterior angles b. alternate interior angles c. consecutive interior angles corresponding angles 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)? same line b. perpendicular c. neither perpendicular nor parallel parallel 3

4 18. In the figure, l Ä n and r is a transversal. Which of the following is not necessarily true? 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? 8 2 b. 2 6 c In the figure shown, HC Ä GD and m ABC = 100. Which of the following statements is false? 12 b. 16 c What is the slope of the line that passes through points A (-2,-3) and B (5,3)? b. 6 c m CBE = 80 b. m DEF = 80 c. 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? neither parallel nor perpendicular b. same line c. parallel perpendicular 23. Which best describes the relationship between Line 1 and Line 2? Line 1 passes through Ê Ë Á 3, 6 ˆ and Ê Ë Á 7, 11 ˆ Line 2 passes through Ê Ë Á 1, 8 ˆ and Ê Ë Á 4, 4 ˆ perpendicular b. They are the same line. c. parallel neither perpendicular nor parallel 24. A line L 1 has slope 4 9. The line that passes through which of the following pairs of points is parallel to L 1? (6, 3) and (2, 6) b. (12, 1) and (2, 8) c. ( 5, 2) and (6, 6) ( 3, 2) and (6, 6) 4

5 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. 26. Write an equation that is parallel to y = 2 3 x 7. y = 3 2 x + 7 b. y = 2 3 x + 1 c. y = 3 2 x + 2 y = 2 3 x Write an equation that is perpendicular to y = 4x + 2. y = 4x + 2 b. y = 4x 2 b. c. y = 1 4 x + 1 y = 1 4 x Write an equation in slope-intercept form of the graph shown. c. y = 11 5 x 7 b. y = 5 11 x 7 c. y = 11 5 x 7 y = 5 11 x 7 5

6 29. Name a right triangle. 33. Find the value of x. BDC b. none of these c. ADB ABC 30. A triangle has angle measures of 60, 60, and 60. Choose the term that describes the triangle. Equiangular b. Right c. Obtuse Scalene 31. How many obtuse angles can an isosceles triangle have? 2 b. 3 c Find the value of x: 117 b. 297 c Find the value of x. 14 b. 166 c Use the figure below to solve for x. 127 b. 35 c b. 90 c

7 36. Refer to the figure below. m C =. 100 b. 17 c Which pair of lengths can be two of the sides of an isosceles triangle which has a perimeter of 52 inches? 15 inches, 25 inches b. 15 inches, 22 inches c. 12 inches, 22 inches 16 inches, 21 inches 39. What is the value of z? (The figure may not be drawn to scale.) 37. The measure of B is. 99 b. 89 c z = 56 b. z = 25 c. z = 64 z = The two triangle-shaped gardens are congruent. Find the missing side lengths and angle measures. a = 5 ft; b = 28 ; c = 90 ; d = 62 ; e = 5 ft b. a = 5 ft; b = 28 ; c = 62 ; d = 90 ; e = 5 ft c. 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

8 41. If ABC DEF, AB = 10 feet, m B = 27, and m F = 14, which of the following statements is false? AC = DF b. C F c. m E = 139 AB = DE 42. In the diagram, B E and C F. Find the value of x. 46. Identify the coordinates of the image point formed after ( 1, 3) is reflected over the x-axis. ( 1, 3) b. (1, 3) c. (1, 3) ( 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? x = 50 b. x = 25 c. x = 75 x = If MNO VWX, which statement is NOT true? NO VW b. O X c. MO VX N W 44. Given: B E and C F. What other piece of information is needed to show ABC DEF by ASA Congruence Postulate? EF FE b. BC EF c. A D B = F 45. In ABC, if AB BC and m A = 39, then m C =. 102 b. 39 c. m B b. 140 c In ABC, AB = 3x 2, BC = x + 4, and AC = 7. Also AB BC. Which term does NOT describe ABC? Equilateral b. Acute c. Isosceles Obtuse 49. Given: ABC DEF with AB BC. Which statement of congruence is not provable? ABC CBA b. DEF CBA c. ABC FDE ABC FED 8

9 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 Ê Ë Áx, yˆ (x+ 4, y+ 3)? ( 7, 9) b. (1, 9) c. ( 7, 3) (1, 3) NO = 3 b. NO = 19 3 c. NO = 7 6 NO = 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 HIL KJL by HL c. HKI HJK by SAS b. HLK JLK by SSS There are no congruent triangles. 53. Refer to the figure shown. Which of the following statements is true? TUV XWV by ASA c. TUV WXV by SAS b. TUV VWX by SAS TUV WXV by SSS 9

10 54. Identify the coordinates of the point ( 5, 3) after a rotation of 180 clockwise about the origin. ( 5, 3) b. (5, 3) c. ( 3, 5) (5, 3) 55. Which graph represents a reflection in the x-axis? 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? reflection over the north-south axis b. rotation c. translation reflection over the east-west axis 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. c. Ê Ë Áv,0ˆ b. (0,u) c. (0,v) Ê Ë Áu,vˆ 58. For the triangle shown, VS = 5 and VQ = 6. Then PQ =. 11 b. 12 c

11 59. Solve for x given BD = 5 x + 4 and AE = 6x 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? AE BE b. AOE EAO c. OA OB AEO BEO 1 2 b. 4 c Given: BC is the perpendicular bisector of KM. Which statement is true? 62. If a b = c, then. d a + b = c + b b d b. ac = bd c. a + b = c + d b d a b = a + c b + d 63. A map has a scale of 1 inch : 28 miles. If the 2 actual distance between the two cities is 448 miles, how far apart are they on the map? 16 inches b. 32 inches c. 8 inches 4 inches BLM, MLC, CLK, KLB are all right angles. b. CM = BM c. KBM is a right angle. C is the midpoint of KM 11

12 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 8 in. = 1 m 3 b. 4 in. = 1 m 1 c. 8 in. = 1 m 7 16 in. = 1 m 65. Are the two polygons similar? (They are not drawn to scale, but assume all angles are 90.) If not, explain why. 67. If two polygons are SIMILAR, then the corresponding sides must be. proportional b. congruent c. parallel similar 68. Given that ABC DEF, solve for x and y. x = 9.75, y = 11.2 b. x = 8.75, y = 11.2 c. x = 8.75, y = 10.2 x = 9.75, y = The perimeter of PQR is 80, PQ = 30, PQR STU, and ST = 18. What is the perimeter of STU? 18.4 b. 6.8 c Yes b. No; c. not enough information to tell 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? 9 mm b. 6 mm c. 3 mm 4 mm No; If two polygons are SIMILAR, then the corresponding angles must be. complementary b. supplementary c. congruent linear pairs 12

13 71. The triangles below are similar. Find x. 73. Two ladders are leaning against a wall at the same angle as shown. 2.9 b. 130 c Which triangle is NOT similar to any of the others? b. c. How far up the wall does the shorter ladder reach? 16 ft b. 18 ft c. 22 ft 36 ft 74. One way to show that two triangles are similar is to show that. 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 an angle of one is congruent to an angle of the other 75. The postulate or theorem that can be used to prove that the two triangles are similar is. SAS Similarity Theorem b. ASA Congruence Theorem c. SSS Similarity Theorem AA Similarity Postulate 13

14 76. If the corresponding sides of two triangles are proportional, then. the triangles are right triangles b. the triangles are similar c. corresponding side lengths are equal the triangles are congruent 77. Given: PQ BC. Find the length of AQ. 79. For the figure shown, which statement is not true? w y = x z b. wx = yz c. wz = xy w x = y 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? 17 b. 19 c If ABC ~ PBQ, then which of the following proportions is NOT true? b. c. AC PQ = CB QB AP PB = AC PQ AP PB = CQ QB PB AB = PQ AC 2 3 b. 3 2 c

15 81. One triangle is shown on the coordinate gri 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? In the figure below, ABC A' B ' C '. Ê Ë Á 7, 7ˆ b. Ê Ë Á 7, 2ˆ c. Ê Ë Á 7, 5ˆ Ê Ë Á 7, 5ˆ 82. Which statement is true of the transformation from ABC to A' B ' C '.? The measures of all corresponding angles change by a scale factor of 2. b. The measures of all corresponding angles change by a scale factor of 1 2. c. The lengths of all corresponding sides change by a scale factor of 2. The lengths of all corresponding sides change by a scale factor of For the triangle shown below, the Pythagorean Theorem states that. e 2 + f 2 = g 2 b. e = f + g c. f 2 g 2 = e 2 e 2 = f 2 + g 2 15

16 84. If a, b, and c are sides of a right triangle, which of the following are also sides of a right triangle? The square root of each length ( a, b, c ) b. Twice the length of each side (2a, 2b, 2c) c. Four more than each length (a + 4, b + 4, c + 4) The square of each length 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. 85. Which of the following sets of numbers is a Pythagorean triple? 3, 4, 5 b. 12, 16, 20 c. 1 3, 1 4, , 4 2, A set of Pythagorean triples is. 3, 5, 9 b. 1, 1, 2 c. 6, 9, 12 5, 12, A 25.5 foot ladder rests against the side of a house at a point 24.1 feet above the groun The foot of the ladder is x feet from the house. Find the value of x to one decimal place. 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? about 29.6 feet b. about 27.6 feet c. about 25.3 feet about 26.3 feet 89. Which set of lengths cannot form a right triangle? 6 mm, 12 mm, 13 mm b. 5 mm, 12 mm, 13 mm c. 2.5 mm, 6 mm, 6.5 mm 10 mm, 24 mm, 26 mm 1.9 b. 7.0 c If the side lengths of a triangle are 7, 6, and 9, the triangle. is an obtuse triangle b. is a right triangle c. is an acute triangle cannot be formed 91. Choose the set that is the possible side lengths of a right triangle. 1, 1, 2 b. 1, 1, 2 c. 3, 4, 7 3, 5, 9 16

17 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? 95. An equilateral triangle has side lengths of 10. The length of its altitude is b. 5 c The tangent of B is. b c feet b. 5.3 feet c. 6.8 feet 2 feet 97. The cosine of A is the ratio. 93. Choose the set that is the possible side lengths of a right triangle. 4, 9, 13 b. 2, 2, 2 c. 1, 1, 2 8, 15, Which of the following cannot be the lengths of a triangle? 21 13, 42 13, b. 23, 46, 46 3 c. 27, 54, , 12, 6 3 b. c. adj. hyp. opp. hyp. hyp. adj. opp. adj. 17

18 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? 154 m b. 59 m c. 61 m 152 m 99. A slide 4.1 m long makes an angle of 27 with the groun How high is the top of the slide above the ground? 1.86 m b m c m 2.09 m 100. Which statement is true? All quadrilaterals are squares. b. All rectangles are squares. c. All parallelograms are quadrilaterals. All quadrilaterals are parallelograms Find tan B for the right triangle below: b. c Find x. Round the result to the nearest hundredth What is x to the nearest hundredth? (not drawn to scale) x = b. x = c. x = x = x = b. x = c. x = x = Which of the following is NOT enough information to solve a right triangle? Two sides b. One side length and one trigonometric ratio c. Two angles One side length and one acute angle measure 105. Find the measure of each exterior angle of a regular polygon with 16 sides b. 360 c

19 106. Choose the statement that is NOT ALWAYS true. For any parallelogram. the diagonals bisect each other b. opposite angles are congruent c. the diagonals are perpendicular opposite sides are congruent 111. Identify two chords 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. IJ and KL b. GH and KL c. GH and IJ GI and HJ x = 1 2 ; y = 13 2 b. x = 8; y = 2 c. x = 8; y = 1 2 x = 2; y = Choose the statement that is NOT ALWAYS true. For a rhombus. each diagonal bisects a pair of opposite angles b. all four sides are congruent c. the diagonals are congruent the diagonals are perpendicular 109. The diagonals of a parallelogram always. are congruent b. are parallel c. bisect each other are perpendicular 110. Which statement is NOT always true of a rhombus? The diagonals are perpendicular to each other. b. The diagonals bisect each other. c. Each diagonal is longer than at least one side. The sum of the diagonals is less than the perimeter A circle is the set of all points in a plane that. have a center b. are equidistant from a given point c. have a diameter lie within a given radius 113. A segment with endpoints on a circle is a. secant b. radius c. tangent chord 114. The center of a circle lies on. every diameter b. the circle c. a tangent line every chord 115. If a circle has a diameter of 12, then it has. a radius of 4 b. a radius of 24 c. a radius of 6 a diameter of A line which intersects a circle at exactly one point is called. a point of tangency b. a tangent line c. a chord a secant 19

20 117. 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 wooden wagon wheel has 12 equally spaced spokes radiating from the central hub. 120 b. 98 c Use the figure. SR is tangent to ñq at R. Choose the true statement. m RQS + m QSR = 180 b. m RQS= 90 c. m SRQ = 90 SQ SR What is the measure of the angle that determines the separation between two adjacent spoke holes? 22.5 b. 30 c Find the value of x RP is tangent to ñg at P. RQ is tangent to ñg at Q. Choose the statement that is NOT true. GRP GRQ b. PGR QGR c. PR QR GPR is obtuse b c

21 122. Given AC bisects BD, choose the true statement that refers to the figure. CD = BA b. BCD is a major arc. c. AC is a diameter. BAD is a minor arc Write the standard equation of a circle with its center at the origin and radius 3. x 2 + y 2 = 6 b. x y 2 6 = 1 c. x 2 + y 2 = 9 x 2 + y 2 = A rectangle has length l and width w. An expression for its area is. 2(l + w) b. l 2 + w 2 c. l w lw 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? 128 times b. 8 times c. 64 times 640 times 127. For a circle of radius 5 feet, find the length of an arc s with a measure of 28. s = 7 9 π feet b. s = 7 18 π feet c. s = 1 36 π feet s = 140π feet 128. Find the length of a 40 arc in a circle with a radius of 4. 8π 9 b. 8π c. 9π 8 16π 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 The area of the parallelogram is. 680 sq. units b. 800 sq. units c sq. units 340 sq. units 24 8π b π c π π 21

22 130. 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? 110 b. 108 c Find the exact volume of a cylinder that has a height of 18 inches and a radius of 8 inches. 384π in 3 b. 288π in 3 c. 1152π in 3 144π in Find the volume of the right triangular prism Find the area of the shaded region cm 2 b cm 2 c cm cm Find the area of an equilateral triangle with side length b. 42 c 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? 32 cubic feet b. 36 cubic feet c cubic feet 12.5 cubic feet 210 m 3 b. 31 m 3 c. 105 m m 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? π( 4) 2 ( 14) 38 b. π( 4) 2 ( 14 3) 38 c. π( 2) 2 ( 14 3) 38 π( 2) 2 ( 14) 3( 2)

23 137. The pyramid shown has a rectangular base and faces that are isosceles triangles. Find its volume. 80 ft 3 b. 240 ft 3 c. 34 ft ft 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 Find the volume of a sphere 4 ft in diameter. Use π 3.14 and round your answer to the nearest tenth ft 3 b ft 3 c ft ft What is the volume of a sphere with diameter 9.4 feet? ft 3 b ft 3 c ft ft 3 Simplify: b c b. 5 2 c Simplify: What is the volume of the foam? cm 3 b cm 3 c cm cm b. 4 5 c b c

24 b. 16 c Simplify: 146. b. c 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

25 ID: A Accelerated Geometry Summer Assignment Answer Section 1. C 2. C 3. C 4. D 5. D 6. D 7. C 8. D 9. C 10. C 11. B 12. A 13. A 14. A 15. D 16. A 17. D 18. D 19. C 20. B 21. B 22. A 23. A 24. D 25. D 26. B 27. C 28. A 29. D 30. A 31. D 32. D 33. D 34. A 35. D 36. B 37. D 38. B 39. C 40. D 41. C 42. B 1

26 ID: A 43. A 44. B 45. B 46. D 47. A 48. D 49. C 50. B 51. D 52. A 53. C 54. B 55. B 56. C 57. C 58. C 59. B 60. A 61. B 62. C 63. C 64. D 65. D 66. C 67. A 68. B 69. C 70. C 71. C 72. D 73. B 74. A 75. D 76. B 77. D 78. B 79. B 80. D 81. C 82. D 83. D 84. B 85. B 86. D 87. C 2

27 ID: A 88. A 89. A 90. C 91. B 92. B 93. B 94. B 95. D 96. A 97. A 98. C 99. A 100. C 101. D 102. D 103. C 104. C 105. C 106. C 107. C 108. C 109. C 110. C 111. C 112. B 113. D 114. A 115. C 116. B 117. B 118. C 119. D 120. B 121. C 122. C 123. C 124. C 125. A 126. C 127. A 128. A 129. D 130. B 131. B 132. D 3

28 ID: A 133. B 134. C 135. C 136. C 137. A 138. B 139. C 140. A 141. B 142. A 143. A 144. C 145. C 146. D 147. b 148. d 4