Preparing for the Regents Examination Geometry, AK

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14 1. ___ DF ___ FE 2. 2 3 3. 1 4 4. ADF CEF (Linear pairs of congruent angles) 5. ADF CEF (ASA ASA) 6. A C (CPCTC) 7. ABC is an isosceles triangle. (Definition of an isosceles triangle) 15 1. ______ AEDC 2. 1 2 3. ___ BE ___ BD 4. AEB CDB 5. ___ AE ___ DC 6. ABE CDB (ASA ASA) 7. A C (CPCTC) 8. ABC is an isosceles triangle. (Definition of an isosceles triangle) 9-8 Proving Right Triangles Congruent by Hypotenuse- Leg; Concurrence of Angle Bisectors of a Triangle (pages 207–208) 1 (a) 2 (d) 3 (c) 4 (b) 5 (a) 6 m1 24, m2 52, m3 104, m4 52, m5 14, m6 114, m7 14, m8 24, m9 142 Note: Since there are many variations of proofs, the following is simply one set of acceptable statements to complete each proof. Depending on the textbook used, the wording and format of reasons may differ, so they have not been supplied for the method of congruence applied in each problem. (These solutions are intended to be used as a guide—other possible solutions may vary.) 7 1. ___ SQ ___ PR 2. ___ SA ___ PB 3. SQP and SAP are right angles. 4. SQP and SAP are right triangles. SP ___ SP 5. ___ 6. ___ SQ ___ SA 7. SQP SAP (HL HL) 8. SPQ APS (CPCTC) 9. ___ PT bisects RPB. (Definition of angle bisector) 8 1. ___ AE ___ BC 2. ___ CD ___ AB 3. CDA and CEA are right angles. 4. CDA and CEA are right triangles. 5. ___ AC ___ AC 6. ___ AE ___ CD 7. ACE CAD (HL HL) 9 1. ___ AE ___ BC 2. ___ CD ___ AB 3. AEB and CDB are right angles. 4. AEB and CDB are right triangles. 5. ___ DB ___ EB 6. DBE DBE 7. AEB CDB (Leg–acute angle) 8. ___ AE ___ CD (CPCTC) 10 1. ___ BD ___ AC 2. ___ QS ___ PR 3. BDA and QSP are right angles. 4. BDA and QSP are right triangles. 5. ABC PQR 6. ___ AB ___ PQ (CPCTC) 7. A P (CPCTC) 8. BDA QSP (Hypotenuse– acute angle) 9. ABD PQS (CPCTC) 10. mABD mPQS 11. ___ BD bisects ABC. 12. 1 _ mABC mABD mPQS 2 13. 1 _ mABC 2 1 _ mPQR (Division 2 postulate) 14. mPQS 1 _ mPQR (Transitive 2 postulate) 15. ___ QS bisects PQR. (Definition of angle bisector) 11 1. ___ AB ___ CF , ___ DE ___ CF 2. ABF and CED are right angles. 3. ABF and CED are right triangles. 4. ___ CD ___ AF 5. ___ BE ___ BE 6. ___ CE ___ FB 7. ABF CED (HL HL) AB ___ DE 8. ___ 9-8 Proving Right Triangles Congruent by Hypotenuse-Leg; Concurrence of Angle Bisectors of a Triangle 51
12 1. ___ CE ___ BA , ___ BD ___ AC 2. CEA and BDA are right angles. 3. CEA and BDA are right triangles. 4. ___ AB ___ AC 5. ABC ABC 6. CEA BDA (Hypotenuse–acute angle) 7. ___ CE ___ BD (CPCTC) 13 1. ___ AC ___ BF , ___ ED ___ BF 2. ACB and FDE are right angles. 3. ACB and FDE are right triangles. 4. ___ AC ___ ED 5. ___ BA ___ EF 6. ACB FDE (HL HL) 7. A E (CPCTC) 9-9 Interior and Exterior Angles of Polygons (pages 210–212) 1 Polygon Number of Sides Number of Triangles Sum of Interior Angles 180(n 2) Triangle 3 1 180(1) 180 180 _ 3 Quadrilateral 4 2 180(2) 360 360 _ 4 Pentagon 5 3 180(3) 540 540 _ 5 Hexagon 6 4 180(4) 720 720 _ 6 Heptagon 7 5 180(5) 900 900 _ 7 Octagon 8 6 180(6) 1,080 1,080 _ 8 Nonagon 9 7 180(7) 1,260 1,260 _ 9 Decagon 10 8 180(8) 1,440 1,440 _ 10 24-gon 24 22 180(22) 3,960 3,960 _ 24 n-gon n n 2 180(n 2) 52 Chapter 9: Parallel Lines Measure of Each Exterior 180(n 2) Angle _ n Measure of Each Interior Angle 360 60 _ 120 3 360 90 _ 90 4 360 108 _ 72 5 360 120 _ 60 6 360 128.57 _ 51.43 7 360 135 _ 45 8 360 140 _ 40 9 360 144 _ 36 10 360 165 _ 15 24 180(n 2) _ n 360 _ n
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: 9-7 The Converse of the Isosceles T
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 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 105 and 106:
Chapters 1-5 (pages 446-449) Part I
Page 107 and 108:
Part IV For each question, use the
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20 Score Explanation 6 The followin
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Part II For each question, use the
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Page 117 and 118:
Part III For each question, use the
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Chapters 1-9 (pages 461-463) Part I
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12 Score Explanation 2 31, and an a
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16 Score Explanation 4 DN √ 106
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20 Score Explanation 2 a 3, and an
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17 Score Explanation 4 6 √ 5 , a
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16 Score Explanation 4 mADE 93, mB
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20 Score Explanation Chapters 1-14
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Practice Regents Examination One (p
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36 Score Explanation 4 36, and an a
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32 Score Explanation 2 108, and an
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Part II For each question, use the
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