Preparing for the Regents Examination Geometry, AK

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16 Score Explanation 4 The following proof or another appropriate proof is given. Right angles B and A are congruent because −− AB −− DB and −− AC −−− DC . −−− BW −−− CW . BWA CWD because vertical angles are congruent. Therefore, by ASA ABW DCW. −−− AW −−− DW because of CPCTC. Hence, AWD is isosceles by definition of an isosceles triangle. 3 An appropriate proof with correct conclusion is shown, but one reason is faulty and/or one statement is missing. 2 An appropriate proof with correct conclusion is used, but multiple reasons are faulty or multiple steps are missing or have errors. 1 AWD is isosceles and a reason is given, but no appropriate method is shown. 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. 17 Score Explanation 4 The following proof or another appropriate proof is given. Statements Reasons 1. BC AB 1. Given. 2. mBAC mBCA 2. The measures of the angles opposite unequal sides are unequal. 3. 1 _ mBAC 2 1 _ mBCA 3. Division postulate. 2 4. −−− DA bisects BAC. 4. Given. 5. mDAC 1 _ mBAC 5. Definition of a bisector. 2 6. −−− DC bisects BCA. 6. Given. 7. mDCA 1 _ mBCA 7. Definition of a bisector. 2 8. mDAC mDCA 8. Substitution postulate. 9. DC DA 9. The lengths of the sides opposite two unequal angles of a triangle are unequal. 3 An appropriate proof with correct conclusion is shown, but one reason is faulty and/or one statement is missing. 2 An appropriate proof with correct conclusion is used, but multiple reasons are faulty or multiple steps are missing or have errors. 1 DC DA and a reason is given, but no appropriate method is shown. 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Chapters 1–7 111
Part IV For each question, use the specific criteria to award a maximum of 6 credits. 18 Score Explanation 1 a (4, 1) 1 b √ 10 2 c y 3x 13 2 d Slope −−− MD 112 Cumulative Reviews 1 _ , slope of the median is 3. The slopes are negative 3 reciprocals; therefore, the median is perpendicular to −−− MD . 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. 19 Score Explanation 4 a Altitude from D to −− AC is x 0. Altitude from C to −−− AD is y 1 _ x 3. 2 Altitude from A to −−− CD is y x 3. 3 a An appropriate method is used, but one computational error is made. 2 a An appropriate method is used, but multiple computational errors are made. 1 a The altitudes are identified, but no explanation is given. 2 b (0, 3), and appropriate work is shown. 1 b (0, 3), but no work is shown. 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. 20 Score Explanation 6 The following proof or another appropriate proof is given. Statements Reasons 1. ABC, −− AB −− BC 1. Given. 2. ABC is isosceles. 2. Definition of isosceles triangle. 3. A C 3. Definition of isosceles triangle. 4. mC mT 4. Definition of an exterior angle. 5. mA mT 5. Substitution postulate. 6. PT AP 6. Greater side opposite greater angle. 5 An appropriate proof with correct conclusion is shown, but one reason is faulty and/or one statement is missing. 4 A faulty conclusion or no conclusion is drawn from the statements and reasoning. 3 An appropriate proof with correct conclusion is shown, but two reasons are faulty or two steps are missing. 2 An appropriate proof with correct conclusion is used, but multiple reasons are faulty or multiple steps are missing or have errors.
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ANSWER KEY Preparing for the REGENT
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Contents Chapter 1: Essentials of G
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1-4 Angles (pages 9-10) 1 (4) It is
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6 True 7 True 8 True 9 True 10 Answ
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3 1. e ∨ ~f 2. ~f → g 3. ~e 4.
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CHAPTER 3 3-1 Inductive Reasoning (
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6. BAC DAE 6. Transitive property.
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CHAPTER 4-1 Setting Up a Valid Proo
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6 Given: BA bisects CBE 1 2 2 4
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1 1. −−−− ABCD 2. 1 2 3. _
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18 1. I is the midpoint of −− E
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5-3 Isosceles and Equilateral Trian
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12. −−− HG −−− DC 13.
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5 1. −− FG is the perpendicular
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Chapter Review (pages 84-85) Note:
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20 Use constructing congruent angle
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6-3 Line Reflections and Symmetry (
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11 A(0, 8), B(2, 2), C(6, 4) (8) 10
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5 (3) (x, y) → (x, 2y) 6 (1) tran
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11. mABC mADC 12. 2mABD 2mADB 13.
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6. mDAB mCAD mDCB mACD 7. mCAB
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g e 17 a _ f d b Undefined c a _
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5 BIG is isosceles because it has t
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___ 27 a M KA (5, 1), M ___ AT (4
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8 106 9 mA 75, mC 67 10 57 11 60
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9-5 The Sum of the Measures of the
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9-7 The Converse of the Isosceles T
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12 1. ___ CE ___ BA , ___ BD ___
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12 a mx 45, my 45 b mx 98, my 8
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Quadrilaterals 10-2 The Parallelogr
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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 and 94: 5 Two horizontal lines y 11 and y
Page 95 and 96: Each review has a total of 58 possi
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 109 and 110: 20 Score Explanation 6 The followin
Page 113: Part II For each question, use the
Page 117 and 118: Part III For each question, use the
Page 123 and 124: 12 Score Explanation 2 31, and an a
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 135 and 136: 16 Score Explanation 4 mADE 93, mB
Page 137 and 138: 20 Score Explanation Chapters 1-14
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
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Preparing for the Regents Examination Geometry, AK

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