chapter 1 basics of geometry answer key

Chapter 1 – Basics of Geometry Answer Key

CK-12 Geometry Concepts 1

1.1 Basic Geometric Definitions

Answers

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



9. Always

10. Never

11. Always

12. Sometimes

13. Never

14. Always

15. Sometimes

16. – 20.



1.2 Distance Between Two Points

Answers

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



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 = 21

3, JK = 5

2

3, HK = 8

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



1.3 Congruent Angles and Angle Bisectors

Answers

1. 𝑃𝑆̅̅̅̅

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°



1.4 Midpoints and Segment Bisectors

Answers

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 𝐴𝐵̅̅ ̅̅ = 𝐶𝐷̅̅ ̅̅

18. A square or a rectangle



1.5 Angle Measurement

Answers

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.



9.

10.

11.

12.

For questions 13-16, student answers might be off by 1 or 2 .

13. 40°

14. 122°

15. 18°



16. 87°

17. 𝑥 = 10°

18. 𝑥 = 22°

19. 𝑥 = 2°

20. 𝑥 = 24°



1.6 Angle Classification

Answers

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.



14. An interior point would be (2, 0).

15. An interior point would be (2, 0).



1.7 Complementary Angles

Answers

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



1.8 Supplementary Angles

Answers

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°



1.9 Linear Pairs

Answers

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.



1.10 Vertical Angles

Answers

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°



1.11 Triangle Classification

Answers

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



15. This triangle is to scale

16. Use #8 to help you. It is the same construction, but do not draw the third side.



1.12 Polygon Classification

Answers

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



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



For questions 18-21 answers will vary

18. 19.

20. 21. A rhombus or diamond

chapter 1 basics of geometry answer key

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