Answer Key. 1.1 Basic Geometric Definitions. Chapter 1 Basics of Geometry. CK-12 Geometry Concepts 1

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1 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 A Circle 5. PQ intersects RS at point Q 6. Always 7. Sometimes 8. Sometimes CK-12 Geometry Concepts 1

2 9. Always 10. Never 11. Always 12. Sometimes 13. Never 14. Always 15. Sometimes CK-12 Geometry Concepts 2

3 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 in cm in cm 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

4 9. BC = 8 cm, BD = 25 cm, CD = 17 cm 10. x = 3, HJ = 21, JK = 12, HK = x = 11, HJ = 52, JK = 79, HK = x = 1, HJ = 2 1, JK = 5 2, HK = x = 17, HJ = 27, JK = 153, KH = x = 16, HJ = 7, JK = 15, KH = Possible Answer units units units units CK-12 Geometry Concepts 4

5 1.3 Congruent Angles and Angle Bisectors 1. PS x = x = True 8. False 9. False; it divides an angle into two congruent angles 10. True 11. Possible Answer 12. m QOP = m QOT = m ROQ = m SOP = 70 CK-12 Geometry Concepts 5

6 1.4 Midpoints and Segment Bisectors in 3. 5 in 4. 5 in in in in 8. 8 triangles cm 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

7 1.5 Angle Measurement 1. m LMN = x = False, B is the vertex 4. True 5. True 6. False, it is equal to the sum of the smaller angles within it CK-12 Geometry Concepts 7

8 For questions 13-16, student answers might be off by 1 or CK-12 Geometry Concepts 8

9 x = x = x = x = 24 CK-12 Geometry Concepts 9

10 1.6 Angle Classification 1. False, two angles could be 5 and 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

11 14. An interior point would be (2, 0). 15. An interior point would be (2, 0). CK-12 Geometry Concepts 11

12 1.7 Complementary Angles (x + y) x or (90 x) 8. m KNJ = m KNJ = False, they add up to False, they can be the sum of any two angles where their sum is False 13. True 14. True 15. True CK-12 Geometry Concepts 12

13 1.8 Supplementary Angles (x y) (x + y) 8. Possible Answer JNI and INM True 11. True 12. False 13. False, all three angles are supplementary 14. x = x = 10.5 CK-12 Geometry Concepts 13

14 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 x or (180 x) 12. x = x = x = * x = * 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

15 1.10 Vertical Angles 1. Possible Answer INJ and MNL 2. m MNL = True 4. False 5. True 6. x = 4, y = 3 7. x = 67, y = x = 38, y = x = x = 11, y = CK-12 Geometry Concepts 15

16 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 No, same reasoning as #7. Two obtuse angles would add up to be greater than 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

17 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

18 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 diagonals 9. 5 diagonals diagonals CK-12 Geometry Concepts 18

19 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

20 For questions answers will vary A rhombus or diamond CK-12 Geometry Concepts 20

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