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Selected AnswersforCore Connections Integrated II

Lesson 1.1.11-4.REFL ONLY:A, B, C, D, E, M, T, U, V, W, Y; ROT. ONLY: N, S, Z;H, I, O, X; OUTSIDE BOTH REGIONS: F, G, J, K, L, P, Q, RINTERSECTION:1-5.a:45;y b: MU 45x 9541 6.40 unitsc: One is a ratio (slope), while the other is a length (distance).1-6.a: isosceles triangle1-7.a: x 61-8.Perimeter: 74 cmArea: 231 cm2b: equilateral triangleb: x 16c: parallelogramc: x 1.5d: x 8Lesson 1.1.21-16. C1-17. isosceles: (a) and (c); scalene: (b)1-18. Multiply the numbers on the sides to get the number on the top. Add the numbers on thesides to get the number on the 3–71-19. It assumes that everyone who likes bananas is a monkey.1-20. Carol: only inside circle #2Bob: outside both circlesPedro: only inside circle #1Toby: intersection of both circles2 2006 - 2016 CPM Educational Program. All rights reserved.Core Connections Integrated II

Lesson 1.2.11-25. Yes, his plants will be dead. If his plants are indoors, they will be dead, because he hasbeen gone for two weeks, so they have not been watered at least once a week. If he leftthem outdoors, they will still be dead, because it has not rained for two weeks, and theywere not watered once a week.9 31-26. a: x – 3311b: x 1c: x 12131-27. a: possibleb: Not possible, because the sum of the measures of an obtuse and right angle is morethan 180 .c: Not possible, because a triangle with all sides of equal length obviously cannot havesides of different lengths.d: possible1-28. a:b:–666–11–51-29. a:12Selected �7parallelogram and square 2006 - 2016 CPM Educational Program. All rights reserved.3

Lesson 1.2.21-36. Part (c) is correct. x 10 cm1-37. a: 33 sq cmb: 33x sq unitsy1-38. a: x 8b:xy–2–50–42–34–26–180x101c: It is the point where the line intersects the x-axis on thegraph. It is the x-value when y 0 in the table.1-39. This reasoning is incorrect. Rewrite “it is raining” in the lower left oval, and “Andrea'sflowers must be closed up” in the right oval.1-40. a: x 18b: x 31-41. a: Sandy’s probability 24c: x 6, while Robert’s is35d: x 2; therefore, Robert has a greater chance.b: Sandy’s probability 1 while Robert’s is 0; therefore Sandy has a greater chance.c: Sandy’s probability 43 , while Robert’s isa shape with two sides that are parallel.435; therefore, Sandy is more likely to select 2006 - 2016 CPM Educational Program. All rights reserved.Core Connections Integrated II

Lesson 1.2.31-50. a: 2x 8b: 2x 4y 81-51. a: 77 56 33 24 190 square unitsb: 33x2 44x – 6x 8 33x2 50x 8 sq. units1-52. a: (3)b: (5)1-53. a: isosceles triangled: scalene trianglec: (6)d: (2)b: regular pentagonc: parallelograme: isosceles right trianglef: trapezoidc: 1200(0.8) 2 1875b: 1200(0.8)3 614.401-54. a: 0.8d: y 1200(0.8)x, where y is the cost and x is the time in years1-55. 9x2 2x 1a: 6, 3b: –2Lesson 1.2.41-62. a: ( 6, 3)b: The vertices are: (6, 2), (2, 3), (5, 6)c: (8, 4)1-63. The graph is flat S-shaped and increasing everywhere (left to right); x-intercept is (8, 0);y-intercept is (0, –2); any value can be input, and any value can be the output; there is nomaximum or minimum; (0, –2) is a special point, because that is where the “S” turnsdirection; it is a function; there are no lines of symmetry.1-64. a: Graph 3, continuous, decreasingb: Graph 2, increasing in “steps”c: Graph 4, increasing, not constant, more rapidly in the middle than beginning or end1-65. a: About 73% a year.b: y 500(0.27)x; x is the number of years after the peak; y is the value x years after thepeak, 500 is the peak value of the poster, and 0.271 is the multiplier for a yearlydecrease of 73%.1-66. a: 420 square units1-67. a:b:–43Selected Answersc:–4–4–8d:–3316–14b: 80 square units–7–3118 2006 - 2016 CPM Educational Program. All rights reserved.–1765

Lesson 1.3.11-75. a: linear pair or straight angle pair, supplementaryb: vertical angles, congruentc: complementaryd: congruent1-76. No, this is not convincing. While the facts are each correct, the conclusion is not basedon the facts. As stated in Fact #2, a square is a rectangle because it has four right angles.However, a rhombus does not have to have four right angles; therefore, there is notenough evidence that a rhombus is a rectangle.1-77. a: Vertical angles, equal measure; 3x 5º 5x – 57º, x 31º; 3(31º) 5º 98º and5(31º) – 57º 98ºb: Straight angle pair, supplementary; 2x 4x 150º 180º; x 5º; 4(5º) 150º 170ºand 2(5º) 10º, 170º 10º 180º1-78. (4x 5)(2x 3) 8x2 22x 15b: f(t) 27000(0.85)t1-79. a: 0.85c: 11,9801-80. a: It should be a triangle with horizontal base of length 4 and vertical base of length 3.b: –c: Any equation of the form y –4343x b.Lesson 1.3.21-87. See answers below.a:KITEb:c:d:ISOSCELES TRIANGLEEQUILATERAL TRIANGLERHOMBUS1-88. a: 238 square unitsb: 112 square units1-89. a: squareb: (–4, 5), (1, 5), (–4, 0), (1, 0)1-90. If x width, then 2x 2(2x 5) 88; the width is 13 cm.1-91. a: If lines have the same slope, then they are parallel.b: If a line is vertical, then its slope is undefined.c: If lines have slopes23and –32, then they are perpendicular.1-92. V-shaped graph, opening upward. As x increases, y decreases left to right until x –2,then y increases. x-intercepts: (–3, 0) and (–1, 0). y-intercept: (0, 1).Minimum point at (–2, –1).6 2006 - 2016 CPM Educational Program. All rights reserved.Core Connections Integrated II

Lesson 1.3.31-98. a: alt. int. anglesb: vertical anglesc: corresponding angles1-99. a:105 75 105 75 75 105 75 105 d: supplementary and straight angle pair or linear pairb:30 70 80 80 85 95 30 95 85 70 85 95 95 85 100 80 80 100 70 110 110 70 1-100. a: If a shape is an equilateral triangle, then it has 120 rotation symmetry.b: If a shape is a rectangle, then the shape is a parallelogram.c: If a shape is a trapezoid, then the area of the shape is half the sum of its basesmultiplied by its height.1-101. (2x 4)(x 2) 2x2 8x 81-102. A1-103. a: Let x the number of votes for candidate B, x (x – 15,000) 109,000.62,000 votesb: Let x time (years); 14(1.1)x; 14(1.1) 2 11.57c: Let x time (years); 29,000(0.89)4 18,195.25d: Let x time (hours); 6x 10 10x, after 2.5 hours, 25 problems eachSelected Answers 2006 - 2016 CPM Educational Program. All rights reserved.7

Lesson 1.3.41-110. a: x 60 b: x 24 c: Calculate the angle measures using x and check that the three angle measures sum to180º. They are 48º and 36º, 48º 36º 96º 180º.1-111. a: Impossible: Can be rejected using Triangle Inequality or Pythagorean Theorem.b: Possiblec: Impossible: The sum of the angles is 179 .d: Possible (but diagram is very inaccurate)e: Impossible: Third angle must be 59º by Triangle Angle Sum, but side opposite 62ºmust be larger than side opposite 59º by Longest Side, Largest Angle.1-112. a:b:–648–8c:–25–5050d:–124–311-113. x 10 , corresponding with y; y 61 , linear pair and supplementary with 119º1-114. a: (x 1)(x 3) x2 4x 3b: (2x 1)(x 2) 2x2 5x 21-115. a:b: (2, –3)8 2.83 unitsc: ( 1, 6), (x, y) (x, y)8d: (–8, 5) 2006 - 2016 CPM Educational Program. All rights reserved.Core Connections Integrated II

Lesson 2.1.12-6.a: ΔABD ΔCBD by ASA b: ΔABC ΔDCB by SAS c: Cannot be determined because “6” is not on corresponding sides.d: ΔABC ΔBAD by AAS e: Cannot be determined because AAA is not a congruence condition.f: QRS GKH by SSS 2-7.a: heartb: squarec: hexagond: Answers vary.2-8.a: Yes. It has four sides. Slope of AB CD 12 and slope of BC AD –2 so eachpair of consecutive sides is perpendicular and forms 90 angles.b: A′(4, 3), B′(6, 1), C′( 2, 5), and D′( 4, 1)2-9.A 26 sq m, P 13 y20 17 21.6 m2-10. See graph at right. (–2, –1)x2-11. In theory, 3 x 13, but some of these lengths are not practical.Selected Answers 2006 - 2016 CPM Educational Program. All rights reserved.9

Lesson 2.1.22-17. a:Given(Def. of isosceles)Def. ofmidpointSegment is to itselfΔYES ΔYEMSSS S M s partsb: Yes; If a triangle is isosceles, then its base angles are congruent.2-18. a: A 31 sq ftb: A 41.5 sq ft2-19. This reasoning is correct.2-20. a: x 3b: no solutionc: x 6d: x 0.52-21. a:b:c:d:358103153145272-22. a: x 17.5º (corresponding angles) 5x 7º 94.5º, 9x – 63º 94.5ºb: x 5º (multiple relationships possible) 12x – 14º 46º, 5x 21º 46º,20x 34º 134º10 2006 - 2016 CPM Educational Program. All rights reserved.Core Connections Integrated II

Lesson 2.1.32-27. a: Converse: If the ground is wet, then it is raining. Not true.b: Converse: If a polygon is a rectangle, then it is a square. Not true.c: Converse: If a polygon has four 90 angles, then it is a rectangle. Not true, it couldhave more than four angles.d: Converse: If a polygon is a triangle, then it has three angles. True.e: Converse: If vertical angles are congruent, then two lines intersect. True.2-28. a: 110 b: 70 c: 48 d: 108 2-29. b: The measure of an exterior angle of a triangle equals the sum of the measures of itsremote interior angles.c:a b c 180 x c 180 Triangle AngleSum TheoremLinear pairsupplementarya b c x cSubstitutiona b xSubtraction Property2-30. a: (–2, 3)b: (–2, 3); yes2-31. a: congruent (HL or SAS )b: congruent (AAS )d: congruent (SAS )c: not necessarily congruent2-32. a:b:28–4–7–11Selected Answersc:–126–24–8d:–16–15.5 2006 - 2016 CPM Educational Program. All rights reserved.11

Lesson 2.1.42-40. Describe a pair of parallel lines.2-41. a: x 425 8.4b: m 22c: t 12.5d: x 32 1.52-42. a: Yes, because of AAS or ASA . ΔDEF ΔLJKb: One possible answer, a reflection across line segment EF and then a translation ofΔDEF so that points J and E′ coincide, followed by a rotation about point E′.2-43. Perimeter 10 10 4 3 4 3 4 38 units, height of triangle 8 units, area 60square units2-44. The longer side of a triangle is opposite the larger angle: m ADB m DAB, soAB DB. And m DCB m BDC, so DB BC. AB 10 and BC 10, so AB BC.2-45. a: There are 10 combinations: a & b, a & c, a & d, a & e, b & c, b & d, b & e, c & d, c &e, d & eb: Yes. If the outcomes are equally likely, we can use the theoretical probabilitycomputation described in the Math Notes box.c:d:310910e: The outcomes that satisfy part (d) include the outcomes that satisfy part (c), but thereare others on the part (d) list as well.12 2006 - 2016 CPM Educational Program. All rights reserved.Core Connections Integrated II

Lesson 2.2.12-51. a: AB 5, BC 4, AC 3b: A′B′ 100 10 units, B′C′ 8 units, and A′C′ 6 unitsc: A 24 sq. units; P 24 units2-52. a: If a rectangle has base x and height 2x, then the area is 2x2. True.b: If a rectangle has base x and height 3y, then the perimeter is 3xy. False. If a rectanglehas base x and height 3y, then the perimeter is 2x 6y.c: If a rectangle has base of 2 feet and a height of 3 feet, then the area is 864 squareinches. True.2-53. h 5 feet; P 24.2 feet2-54.AC DFGivenm A m DGivenAB DEGivenΔABC ΔDEFSAS 2-55. a: x2 8x 15 (x 3)(x 5)b: 2x2 13x 15 (2x 3)(x 5)2-56. a: x 45º; isosceles right triangleb: 71º y 180º, y 109º; acute isosceles triangleSelected Answers 2006 - 2016 CPM Educational Program. All rights reserved.13

Lesson 2.2.22-61. Result should be 12 units tall and 16 units wide.2-62. a: The 15 corresponds to the 6, while the 20 corresponds to the 8. Multiple equivalent20ratios are possible. One possibility: 156 8 2.5b: 25 and 10;2510 2.5 ; yesc: Possible response: Translate the figure on the right so that the right angle verticescoincide. Rotate the image about the right angle vertex so the legs coincide. Thendilate the image by 2.5 through the vertex.2-63. a: Graph 2b: Graph 3c: Graph 12-64. a: triangle inequalityb: Pythagorean Theoremc: base angles not equal2-65. a:b:c:d:–100–1010–98–147–72-66. a: yes14–33b:25c:35d:15 2006 - 2016 CPM Educational Program. All rights reserved.0e:45Core Connections Integrated II