Preparing for the Regents Examination Geometry, AK

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37 Score Explanation 4 Secant points of intersection are (0, 5) and (2, 4), and an appropriate explanation is given. 3 Secant is given, but graph is incorrect. 2 Graph is shown, but secant is not given. 1 Secant is given, but graph is not shown. 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Part IV For each question, use the specific criteria to award a maximum of 6 credits. 38 Score Explanation 6 Any appropriate method is used to prove that ABCD is a parallelogram, but not a rectangle. For example: showing that the diagonals bisect each other but are not congruent, or showing that no consecutive sides have negative reciprocal slopes. 5 An appropriate method is used, but a single computational error is made. 4 An appropriate method is used, but two computational errors are made. 3 An appropriate method is used to prove that ABCD is a parallelogram but does not show that it is not a rectangle. 2 An appropriate method is used to prove that ABCD is a parallelogram, but more than two computational errors are made and student does not show that it is not a rectangle. 1 An appropriate method is used, but ABCD is not shown to be a parallelogram, and multiple computational errors are made. 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Practice Regents Examination Three (pages 497–504) Part 1 Allow a total of 56 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 (2) 50 2 (4) 16 : 25 3 (4) (7, 7 √ 3 ) 4 (2) 18 cm 2 5 (3) {2, 7, 10} 6 (3) (3, 6.5) 7 (3) 80 √ 3 8 (3) ABCD is a parallelogram whose diagonals bisect each other. 9 (2) 2 _ 3 10 (2) 156 11 (2) (x 3) 2 (y 7) 2 2 12 (3) y 1 _ x 4 2 13 (3) d 5 14 (4) 11 15 (1) 60 16 (2) 32 √ 3 17 (2) 16 16 √ 2 18 (4) x 1 19 (1) 5 20 (2) y 5x 2 21 (3) 4 √ 3 22 (1) perpendicular bisectors of the sides 23 (3) 120 24 (4) obtuse 25 (3) 60 26 (4) 210 27 (1) The perpendicular bisector of the chord of a circle bisects the intercepted arc. 28 (1) (3, 5) Practice Regents Examination Three 143
Part II For each question, use the specific criteria to award a maximum of 2 credits. 29 Score Explanation 2 216 cubic inches, and an appropriate explanation is given. 1 216 cubic inches, 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. 30 Score Explanation 1 a PA 9, and an appropriate explanation is given. 1 b m CB 53 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. 31 Score Explanation 2 16 inches, and an appropriate explanation is given. 1 16 inches, 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. 32 Score Explanation 2 60 _ , and an appropriate explanation is given. 13 1 60 _ , but no explanation is given. 13 0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. 33 Score Explanation 2 32, and an appropriate explanation is given. 1 32, 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. 34 Score Explanation 2 4, and an appropriate explanation is given. 1 4, 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. 144 Practice Geometry Regents Examinations
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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
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27 1. Common external tangents, −
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8. mHCT 1 _ m 2 TH mCHT 1 _ CT 2
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16 a (2 √ 2 , 2 √ 2 ), (2 √
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15 a Use constructing a congruent a
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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
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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: 32 Score Explanation 2 108, and an
Page 149: Part IV For each question, use the
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