Preparing for the Regents Examination Geometry, AK

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19 Score Explanation 6 The following proof or another appropriate proof is given. Statements Reasons 1. Parallelogram ABCD; −−− EAB ; −−− DCF 1. Given. 2. −− AB −−− DC 2. Definition of a parallelogram. 3. −− EB −− DF 3. Collinearity. 4. AEH CFG 4. Alternate interior angles are congruent. 5. BAH BCD 5. Opposite angles of a parallelogram are congruent. 6. GCF and BCD are a linear pair. HAE and BAH are a linear pair. 7. GCF and BCD are supplementary. HAE and BAH are supplementary. 6. Definition of linear pair. 7. Two angles that form a linear pair are supplementary. 8. GCF HAE 8. Supplements of congruent angles are congruent. 9. a EAH FCG 9. AA. 10. EA _ AH FC _ CG 10. Corresponding parts of similar triangles are in proportion. 11. b EA CG AH CG 11. The product of means equals the product of extremes. 5 An appropriate proof with correct conclusion is shown, but one reason is faulty and/or one statement is missing. 4 An appropriate proof with correct conclusion is shown for part a only. 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 more than two reasons are faulty or more than two steps are missing or have errors. 1 EAH FCG and EA CG AH CG, 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 1–13 133
20 Score Explanation Chapters 1–14 (pages 476–479) 1 a m BC 72, and an appropriate explanation is given. 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. 1 b mEDC 108, and an appropriate explanation is given. 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. 1 c mBCR 36, and an appropriate explanation is given. 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. 1 d mAKB 72, and an appropriate explanation is given. 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. 2 e mRF 72, and an appropriate explanation is given. 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Part I Allow a total of 20 credits, 2 credits for each of the following correct answers. Allow credit if the student has written the correct answer instead of the numeral 1, 2, 3, or 4. 1 (1) x 3 2 (3) 3 : 5 3 (3) 125 4 (2) 45 5 (3) 2 √ 2 134 Cumulative Reviews 6 (2) 8.8 7 (2) 2x 3 8 (1) {C, D, G, H} 9 (4) y 3x 5 10 (4) similar triangles Part II For each question, use the specific criteria to award a maximum of 2 credits. 11 Score Explanation 2 720, and an appropriate explanation is given. 1 720, but no explanation is given. 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. 12 Score Explanation 2 144, and an appropriate explanation is given. 1 144, but no explanation is given. 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure.
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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)
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5. RSQ TSV (Vertical angles) 6. QR
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3 4x 2 3x 3 x 5 RS 18 4 Perime
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Note: Since there are many variatio
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28 Enclose PAT in a large rectangle
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Geometry of Three Dimensions 11-1 P
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11-6 Volume of a Prism (pages 269-2
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14 47.5 in. 2 15 h 4 in. 16 25 cm
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14 a 3 : 2 b QR 10, RS 20, ST 12
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4. A A 5. ADE ABC b (AA) AC _ AB
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12 7 √ 2 13 4 14 5 √ 3 15 x
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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 and 114: 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: 16 Score Explanation 4 mADE 93, mB
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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