16 (4) 4 17 (1) 90 x 18 8 19 x 3, PD 6, RP 12, RD 18 20 x 2, y 4, BE 9, AD 12 Note: For exercises 21–24, check students’ sketches. 21 Two concentric circles. Locus: radius 1 and radius 7. 22 Circle, radius 3, x 2 y 2 9. Two lines, x 4, x 4. Locus: 0 points 23 Circle: x 2 y 2 4. Circle: x 2 (y 4) 2 9. Locus: 1 point, (0, 2) 24 Two lines parallel to line m on opposite sides and 4 centimeters from m. Circle with center H and radius 2. Locus: 1 point 25 (x 4) 2 (y 2) 2 1 26 y x 4 27 Two lines: y x 2 and y x 2 Note: For exercises 28–37, check students’ sketches. 28 b (2, 0.5), (5, 1), (1, 1) 2 c y _ x 2x 6 _ 1 3 _ 6 29 b (5, 7), (1, 3), (3, 1) 2 y c x _ 3y 8 _ 1 4 _ 8 30 b (2, 0), (2, 2), (6, 2) x 2 c y _ x 8 _ 2 1 _ 2 31 b (1, 0), (1, 4), (1, 4) y 2 c x _ 1 8 32 (0, 5), (3, 4), (3, 4) 33 (0, 5), (3, 8) 34 (0, 3), (3, 9) 35 (2 √ 7 , 1 √ 7 ), (2 36 (3, 10), (1, 6) √ 7 , 1 √ 7 ) 37 (0, 4), ( √ 7 , 3), ( √ 7 , 3) 38 The intersection of <strong>the</strong> perpendicular bisector of AB, and circle with A as center Case I x 1 _ f (0 points) 2 Case II x 1 _ f (1 point) 2 Case III x 1 _ f (2 points) 2 39 The intersection of one circle with radius of 2.5, concentric with <strong>the</strong> given circles, and two lines parallel to <strong>the</strong> given line, one on each side at a distance x from <strong>the</strong> given line. Case I x 2.5 (4 points) Case II x 2.5 (2 points) Case III x 2.5 (0 points) 40 The intersection of circle with center P and radius d and circle with center Q and radius d. Case I x 2d (2 points) Case II x 2d (1 point) Case III x 2d (0 points) 41 The intersection of two lines parallel to line m, one on each side at a distance d from line m and <strong>the</strong> circle with center A and radius r. Case I r d (0 points) Case II r d (2 points) Case III r d (4 points) 42 Locus: A line parallel to <strong>the</strong> north side and south side of <strong>the</strong> courtyard and midway between <strong>the</strong>m. Since <strong>the</strong> width of <strong>the</strong> garden is 60 ft, every point on this line will be equidistant from <strong>the</strong> north and south walls and at least 30 feet from <strong>the</strong> North Entrance. 43 Check students’ constructions of <strong>the</strong> orthocenter of an acute triangle. 44 Check students’ constructions of <strong>the</strong> perpendicular bisector of <strong>the</strong> three sides of a right triangle. 45 Check students’ constructions of a circle that passes through <strong>the</strong> three vertices of an obtuse triangle. Chapter Review 91
Each review has a total of 58 possible points. Use <strong>the</strong> following table, adapted from <strong>the</strong> <strong>Regents</strong> <strong>Examination</strong>s, to convert <strong>the</strong> student’s raw score to a scaled score. Raw Score Scaled Score Raw Score Scaled Score Raw Score Scaled Score 58 100 38 75 19 49 57 99 37 74 18 47 56 98 36 72 17 46 55 97 35 70 16 45 54 96 34 68 15 44 53 93 33 67 14 43 52 92 32 66 13 42 51 91 31 65 12 41 50 90 30 64 11 39 49 89 29 63 10 37 48 87 28 61 9 36 47 86 27 60 8 34 46 85 26 59 7 32 45 84 25 58 6 29 44 82 24 57 5 26 43 80 23 56 4 21 42 79 22 54 3 16 41 78 21 53 2 10 40 77 20 51 1 5 39 76 Chapters 1–2 (pages 434–437) Part I Allow a total of 20 credits, 2 credits <strong>for</strong> each of <strong>the</strong> following correct answers. Allow credit if <strong>the</strong> student has written <strong>the</strong> correct answer instead of <strong>the</strong> numeral 1, 2, 3, or 4. 1 (4) a → r 2 (2) −− AB 3 (3) p q 92 Cumulative Reviews
- Page 1 and 2:
ANSWER KEY Preparing for the REGENT
- Page 3 and 4:
Contents Chapter 1: Essentials of G
- Page 5 and 6:
1-4 Angles (pages 9-10) 1 (4) It is
- Page 7 and 8:
6 True 7 True 8 True 9 True 10 Answ
- Page 9 and 10:
3 1. e ∨ ~f 2. ~f → g 3. ~e 4.
- Page 11 and 12:
CHAPTER 3 3-1 Inductive Reasoning (
- Page 13 and 14:
6. BAC DAE 6. Transitive property.
- Page 15 and 16:
CHAPTER 4-1 Setting Up a Valid Proo
- Page 17 and 18:
6 Given: BA bisects CBE 1 2 2 4
- Page 19 and 20:
1 1. −−−− ABCD 2. 1 2 3. _
- Page 21 and 22:
18 1. I is the midpoint of −− E
- Page 23 and 24:
5-3 Isosceles and Equilateral Trian
- Page 25 and 26:
12. −−− HG −−− DC 13.
- Page 27 and 28:
5 1. −− FG is the perpendicular
- Page 29 and 30:
Chapter Review (pages 84-85) Note:
- Page 31 and 32:
20 Use constructing congruent angle
- Page 33 and 34:
6-3 Line Reflections and Symmetry (
- Page 35 and 36:
11 A(0, 8), B(2, 2), C(6, 4) (8) 10
- Page 37 and 38:
5 (3) (x, y) → (x, 2y) 6 (1) tran
- Page 39 and 40:
11. mABC mADC 12. 2mABD 2mADB 13.
- Page 41 and 42:
6. mDAB mCAD mDCB mACD 7. mCAB
- Page 43 and 44: g e 17 a _ f d b Undefined c a _
- Page 45 and 46: 5 BIG is isosceles because it has t
- Page 47 and 48: ___ 27 a M KA (5, 1), M ___ AT (4
- Page 49 and 50: 8 106 9 mA 75, mC 67 10 57 11 60
- Page 51 and 52: 9-5 The Sum of the Measures of the
- Page 53 and 54: 9-7 The Converse of the Isosceles T
- Page 55 and 56: 12 1. ___ CE ___ BA , ___ BD ___
- Page 57 and 58: 12 a mx 45, my 45 b mx 98, my 8
- Page 59 and 60: Quadrilaterals 10-2 The Parallelogr
- Page 61 and 62: 7. MAD RCB 8. MAD RCB (SAS SAS)
- Page 63 and 64: 5. RSQ TSV (Vertical angles) 6. QR
- Page 65 and 66: 3 4x 2 3x 3 x 5 RS 18 4 Perime
- Page 67 and 68: Note: Since there are many variatio
- Page 69 and 70: 28 Enclose PAT in a large rectangle
- Page 71 and 72: Geometry of Three Dimensions 11-1 P
- Page 73 and 74: 11-6 Volume of a Prism (pages 269-2
- Page 75 and 76: 14 47.5 in. 2 15 h 4 in. 16 25 cm
- Page 77 and 78: 14 a 3 : 2 b QR 10, RS 20, ST 12
- Page 79 and 80: 4. A A 5. ADE ABC b (AA) AC _ AB
- Page 81 and 82: 12 7 √ 2 13 4 14 5 √ 3 15 x
- Page 83 and 84: 13-2 Arcs and Chords (pages 350-351
- Page 85 and 86: 27 1. Common external tangents, −
- Page 87 and 88: 8. mHCT 1 _ m 2 TH mCHT 1 _ CT 2
- Page 89 and 90: 16 a (2 √ 2 , 2 √ 2 ), (2 √
- Page 91 and 92: 15 a Use constructing a congruent a
- Page 93: 5 Two horizontal lines y 11 and y
- Page 97 and 98: Part III For each question, use the
- Page 99 and 100: Chapters 1-3 (pages 438-441) Part I
- Page 101 and 102: Part IV For each question, use the
- Page 103 and 104: 16 Score Explanation 4 a 91, b 35
- Page 105 and 106: Chapters 1-5 (pages 446-449) Part I
- Page 107 and 108: Part IV For each question, use the
- Page 109 and 110: 20 Score Explanation 6 The followin
- Page 111 and 112: 17 Score Explanation 4 The followin
- Page 113 and 114: Part II For each question, use the
- Page 115 and 116: Part IV For each question, use the
- Page 117 and 118: Part III For each question, use the
- Page 119 and 120: Chapters 1-9 (pages 461-463) Part I
- Page 121 and 122: 19 Score Explanation 6 The followin
- Page 123 and 124: 12 Score Explanation 2 31, and an a
- Page 125 and 126: 20 Score Explanation 6 The followin
- Page 127 and 128: 16 Score Explanation 4 DN √ 106
- Page 129 and 130: 20 Score Explanation 2 a 3, and an
- Page 131 and 132: 17 Score Explanation 4 6 √ 5 , a
- Page 133 and 134: 20 Score Explanation 6 The followin
- Page 135 and 136: 16 Score Explanation 4 mADE 93, mB
- Page 137 and 138: 20 Score Explanation Chapters 1-14
- Page 139 and 140: Part IV For each question, use the
- Page 141 and 142: Practice Regents Examination One (p
- Page 143 and 144: 36 Score Explanation 4 36, and an a
- Page 145 and 146:
32 Score Explanation 2 108, and an
- Page 147 and 148:
Part II For each question, use the
- Page 149:
Part IV For each question, use the