1.1 Basic Geometric Definitions 1. WX, XW, WY, YW, XY, YX and line m. 2. Plane V, Plane RST, Plane RTS, Plane STR, Plane SRT, Plane TSR, and Plane TRS. 3. 4. A Circle 5. PQ intersects RS at point Q 6. Always 7. Sometimes 8. Sometimes CK-12 Geometry Concepts 1
9. Always 10. Never 11. Always 12. Sometimes 13. Never 14. Always 15. Sometimes 16. 20. CK-12 Geometry Concepts 2
1.2 Distance Between Two Points For questions 1-8, your answers may vary, depending on the size of paper you printed these questions on. These answers are for 100% on a 8.5 x 11 piece of paper. 1. 2.75 in 2. 4.9 cm 3. 4.625 in 4. 8.6 cm 5. 6. O is the midpoint. LO = OT = 8 cm. 7. a) b) TA + AQ = TQ c) TQ = 15 in 8. a) b) HM + MA = HA c) MA = 11 cm CK-12 Geometry Concepts 3
9. BC = 8 cm, BD = 25 cm, CD = 17 cm 10. x = 3, HJ = 21, JK = 12, HK = 33 11. x = 11, HJ = 52, JK = 79, HK = 131 12. x = 1, HJ = 2 1, JK = 5 2, HK = 8 3 3 13. x = 17, HJ = 27, JK = 153, KH = 180 14. x = 16, HJ = 7, JK = 15, KH = 22 15. Possible Answer 16. 13 units 17. 5 units 18. 9 units 19. 5 units CK-12 Geometry Concepts 4
1.3 Congruent Angles and Angle Bisectors 1. PS 2. 90 3. 45 4. 45 5. x = 20 6. x = 14 7. True 8. False 9. False; it divides an angle into two congruent angles 10. True 11. Possible Answer 12. m QOP = 100 13. m QOT = 130 14. m ROQ = 30 15. m SOP = 70 CK-12 Geometry Concepts 5
1.4 Midpoints and Segment Bisectors 1. 2. 12 in 3. 5 in 4. 5 in 5. 13 in 6. 10 in 7. 24 in 8. 8 triangles 9. 3.5 cm 10. 2 in 11. (3, -5) 12. (1.5, -6) 13. (5, 5) 14. (-4.5, 2) 15. B is (7, 10) 16. A is (6, 9) 17. This is incorrect. She should have written AB = CD or AB = CD 18. A square or a rectangle CK-12 Geometry Concepts 6
1.5 Angle Measurement 1. m LMN = 32 2. x = 15 3. False, B is the vertex 4. True 5. True 6. False, it is equal to the sum of the smaller angles within it. 7. 8. CK-12 Geometry Concepts 7
9. 10. 11. 12. For questions 13-16, student answers might be off by 1 or 2. 13. 40 14. 122 15. 18 CK-12 Geometry Concepts 8
16. 87 17. x = 10 18. x = 22 19. x = 2 20. x = 24 CK-12 Geometry Concepts 9
1.6 Angle Classification 1. False, two angles could be 5 and 30 2. False, it is a straight angle 3. True 4. True 5. False, a right angle and acute angle add up to greater than 90, but an obtuse angle is just one angle, not two. 6. Acute 7. Obtuse 8. Obtuse 9. Acute 10. Obtuse 11. Acute 12. AE = CD, ED = CB, m EAC = m ABC 13. CK-12 Geometry Concepts 10
14. An interior point would be (2, 0). 15. An interior point would be (2, 0). CK-12 Geometry Concepts 11
1.7 Complementary Angles 1. 87 2. 8 3. 39 4. 60 5. 68 6. 90 (x + y) 7. 90 x or (90 x) 8. m KNJ = 30 9. m KNJ = 20 10. False, they add up to 90 11. False, they can be the sum of any two angles where their sum is 90 12. False 13. True 14. True 15. True CK-12 Geometry Concepts 12
1.8 Supplementary Angles 1. 68 2. 165 3. 83 4. 99 5. 123 6. 180 (x y) 7. 180 (x + y) 8. Possible Answer JNI and INM 9. 117 10. True 11. True 12. False 13. False, all three angles are supplementary 14. x = 17 15. x = 10.5 CK-12 Geometry Concepts 13
1.9 Linear Pairs 1. False, they are supplementary. 2. True 3. False, they are next to each other. 4. True 5. False, they can form linear pairs, but not all the time. 6. 126 7. 158 8. 76 9. 109 10. 31 11. 180 x or (180 x) 12. x = 34 13. x = 17 14. x = 15 15.* x = 11 16.* x = 11.1 (use the Quadratic Formula) *The negative possibilities for x are not solutions because we have not yet introduced negative angles. CK-12 Geometry Concepts 14
1.10 Vertical Angles 1. Possible Answer INJ and MNL 2. m MNL = 53 3. True 4. False 5. True 6. x = 4, y = 3 7. x = 67, y = 30 8. x = 38, y = 25 9. x = 15 10. x = 11, y = 7 11. 113 12. 172 13. 26 14. 20 CK-12 Geometry Concepts 15
1.11 Triangle Classification 1. Acute scalene 2. Equiangular equilateral 3. Right isosceles 4. Obtuse scalene 5. Acute isosceles 6. No, because a right angle is 90 and an obtuse angle is greater than 90. That would be a sum greater than 180 and a triangle s three angles must add up to exactly 180. 7. No, same reasoning as #7. Two obtuse angles would add up to be greater than 180. 8. 9. All the angles in an equilateral triangle must be equal. So, an equilateral triangle is also an equiangular triangle. 10. Sometimes 11. Never 12. Always 13. Sometimes 14. Never CK-12 Geometry Concepts 16
15. This triangle is to scale 16. Use #8 to help you. It is the same construction, but do not draw the third side. CK-12 Geometry Concepts 17
1.12 Polygon Classification 1. Concave pentagon 2. Convex octagon 3. Convex 17-gon 4. Convex decagon 5. Concave quadrilateral 6. Concave hexagon 7. A is not a polygon because two of the sides do not meet at a vertex; B is not a polygon because one side is curved; C is not a polygon because it is not closed. 8. 2 diagonals 9. 5 diagonals 10. 9 diagonals CK-12 Geometry Concepts 18
11. This shows us that the number diagonals from one vertex increase by one each time. So, for an n-gon, there are (n-3) diagonals from one vertex 12. Octagon: 20 total diagonals, Nonagon: 27 total diagonals, Decagon: 35 total diagonals, Undecagon: 44 total diagonals, Dodecagon: 54 total diagonals 13. Always 14. Always 15. Sometimes, a square is ALWAYS a quadrilateral. 16. Sometimes, you can draw AT MOST n 3 diagonals from one vertex. 17. Sometimes, a 5-point star is ALWAYS a decagon CK-12 Geometry Concepts 19
For questions 18-21 answers will vary 18. 19. 20. 21. A rhombus or diamond CK-12 Geometry Concepts 20