Example 4 Name each angle in three ways. QExample …€¦ · 22. a straight angle, ^EFG 23. a...

1.4 – Angles - Homework 1.) Name the angle in four ways. 2.) Name ∠2 in two different ways. 3. Find m∠CBD if m∠ABC = 45° and m∠ABD = 79° 4. Find m∠GFJ if m∠EFG =110°

Example 3 |2 12. Algebra Ais the midpoint ofXY.(page 27) a Find XA.

b.Find AYmdXY.

3x

Example 4(page 27)

Example 5(page 28)

Algebra In Exercises 13-15, use the figure and find FT.

13. PT = 5x + 3 and TQ = Ix - 9

14. PT= 4x- 6 and TQ = 3x + 4

15. PT=lx- 24 and TQ = 6x - 2

Name each angle in three ways.

16. it

Use the figure at the right. Name theindicated angle in two different ways.

18. Z.1 19. Z.2

Draw and label a figure to fit each description.

20. an obtuse angle, ARST 21. an acute acute, ^BCD

22. a straight angle, ^EFG 23. a right angle, AGHI

Measure and classify each angle.

24. y 25.

5x-6

Q

Example 6 27. Find m/LCBD if mAABC = 45(page 29) and m/LABD = 79.

28. YmdmLGFJUm^EFG = 110.

ApplyYourSkills Use the figure at the right for Exercises 29-32.

30

29. Find the midpoint of AB.

30. What is the coordinate of themidpoint of QBl

A S QH 1 h-0 2 4

B

31. What is the coordinate of the midpoint of WAl

32. What is the coordinate of the midpoint of the segment formed by the twopoints you foimd in Exercises 30 and 31?

Suppose the coordinate of A is 0 and AR = 5 and AT = 7 in the figure above.What are the possible coordinates of the midpoint of the given segment?

33. AR 34. AT 35. RT

Chapter 1 Tools of Geometry


b.Find AYmdXY.

3x

Example 4(page 27)

Example 5(page 28)


13. PT = 5x + 3 and TQ = Ix - 9

14. PT= 4x- 6 and TQ = 3x + 4

15. PT=lx- 24 and TQ = 6x - 2


16. it


18. Z.1 19. Z.2





24. y 25.

5x-6

Q




30



A S QH 1 h-0 2 4

B




33. AR 34. AT 35. RT



b.Find AYmdXY.

3x

Example 4(page 27)

Example 5(page 28)


13. PT = 5x + 3 and TQ = Ix - 9

14. PT= 4x- 6 and TQ = 3x + 4

15. PT=lx- 24 and TQ = 6x - 2


16. it


18. Z.1 19. Z.2





24. y 25.

5x-6

Q




30



A S QH 1 h-0 2 4

B




33. AR 34. AT 35. RT



b.Find AYmdXY.

3x

Example 4(page 27)

Example 5(page 28)


13. PT = 5x + 3 and TQ = Ix - 9

14. PT= 4x- 6 and TQ = 3x + 4

15. PT=lx- 24 and TQ = 6x - 2


16. it


18. Z.1 19. Z.2





24. y 25.

5x-6

Q




30



A S QH 1 h-0 2 4

B




33. AR 34. AT 35. RT


In the diagram, m∠ACB = 65° . Find each of the following. 5. m∠BCD 6. m∠ECD Use the figure below for exercises 7-8. 7. If m∠MQV = 90° and m∠VQP = 35° , what is m∠MQP ? 8. If m∠MVQ = 55° , what is m∠QVP ? 9. a. Solve for x if m∠RQS = 2x + 4 and m∠TQS = 6x + 20 .

b. What is m∠RQS ? m∠TQS ? c. Show how you can check your answer.

Need Help?For Exercise 43 you areto decide whether thedistance BD is less thanthe distance CD.

^ 36. Mileage Highways and the mile markers along their sides suggest a numberline. You can find the distance between mile markers in the same way that youfind distance on a number line.a. Michael sees mile marker 237 when he enters the highway and mile marker159 when he exits. How far did he travel?

b. Open-Ended Give another real example of finding distance using anumber hne.

Visualization Without using your ruler, sketch a segment with the given length.Then use your ruler to see how well you did.

37. 3 cm 38. 3 in. 39. 6 in. 40. 10 cm 41. 65 mm

In Exercises 42-45, describe the statementas true or false. Explain.

A B•<» I » I 1

C DI I

42. AB = CD 43. BD < CD

44. AC + BD = AD 45. AC + CD = AD

46. Suppose EG = 5. Find the possible coordinate(s) of point G.

In the diagram, mAACB = 65. Find each of the following.

47. mABCD 48. mAECD

E49. Coordinate Geometry A(3,0) is an

endpoint of AB. If AB = 12, give fourpossible coordinates for point B.

1 3

Exercises 42-46

Exercises 47-48

Visualization Without using your protractor, sketch an angle with the givenmeasure. Then use your protractor to see how well you did.

50. 45 51. 60 52. 90 53. 120

55. Skiing Use a protractor on the photographto measure the angle formed by the two skis.

Open-Ended Name two times of the morning whenthe hands of a clock form each type of angle.

56. right 57. obtuse 58. straight

Estimation Estimate the measure of the angleformed by the hands of a clock at each time.

59. 6:00

62. 4:40

60. 7:00

63. 5:20

61.11:00

64.10:40

Use this figure for Exercises 65-69.

65. If mAMQV = 90 and m^VQP = 35,what is mAMQP7

66. Ifm^MVQ = 55, what is mZgVP? ^ N

Judging by appearance in the diagram above, name each of the following.

67. two acute angles 68. two obtuse angles 69. two right angles

54. 135

Lesson 1-4 iVleasuring Segments and Angles

E

31

Use the diagram below for exercises 10-11. 10.) If AD = 12 and AC = 4y – 36, find the value of y.

Then find AC and DC. 11.) If ED = x + 4 and DB = 3x – 8, find ED, DB, and EB. Use the diagram, below, for exercises 12-15. Solve for x. Find the angle measures to check your work. 12.) m∠AOC = 7x − 2 , m∠AOB = 2x +8 , m∠BOC = 3x +14

Real-World ^ ConnectionJapanese flower arrangingmakes precise use of anglesto create a mood.

Challenge

x^l 70. a.Algebra Solve for x ifm/LRQS = 2x 4and m/^TQS — 6x + 20.

b. What is mARQSI mZ-TQSlc. Show how you can check your answer.

a;7v^'

Ix^l Algebra Use the diagram at the right for Exercises 71and 72.71. If Ai:" = 12 and AC = 4y - 36, findthe value ofy."pien find ACandDC.

72. If ED =x +-4andDfi = 3x - 8,findED, DB, and EB.

%Js 73. Writing The word acute can mean "sharp" in conversational English.

a. Explain why this meaning describes an acute angle.b. Use "acute" in a sentence.

74. Flower Arranging In Japanese flowerarranging, you match a stem that isvertical with 0. You match otherstems with numbers from 0 to90, in both directions from thevertical.What numbers wouldthe flowers shown be pairedwith on a standard protractor?

Algebra Use the diagram, below right, for Exercises 75-78. Solve for x. Find theangle measures to check your work.

75. m^AOC = lx- 2,mAAOB = 2x + 8,mABOC = 'ix + lA

76. mAAOB = 4x - 2,mABOC = 5x + 10,mACOD = 2x + 14

77. mAAOB = 28,mABOC = 3x - 2,m^AOD = 6x

78. mAAOB = 4x + 3,mABOC = 7x,m/LAOD = 16x —1

79. C is the midpoint of AB, D is the midpoint of AC, E is the midpoint of AD,Fis the midpoint of ED, G is the midpoint of EF, and H is the midpoint of DB.If DC = 16, find G//.

80. Golf Copy the diagram.a. Estimate the angle in degrees from the tee holemarked by the flag. Then estimate the distance icentimeters or millimeters from the tee to the h

b. Use a protractor and ruler to plot eachestimate. This is stroke 1.Add a penaltystroke if you land in the water.

c. Continue until you are at most 5mm from thehole marked by the flag.What is your scoi ^''

- yi)^.

32 Chapter 1 Tools of Geometry

13.) m∠AOB = 4x − 2 , m∠BOC = 5x +10 , m∠COD = 2x +14 14.) m∠AOB = 28° , m∠BOC = 3x − 2 , m∠AOD = 6x 15.) m∠AOB = 4x +3 , m∠BOC = 7x , m∠AOD =16x −1

Answer Key 1. ∠1, ∠C , ∠PCM , ∠MCP 2. ∠CBD , ∠DBC 3. 34° 4. 70° 5. 115° 6. 65° 7. 125° 8. 125° 9. a. 19.5

b. 43° ; 137° c. Answers may vary. Sample: The sum of the angle measures should be 180° .

10. y = 15; AC = 24, DC = 12 11. ED = 10, DB = 10, EB = 20 12. 12; m∠AOC = 82° , m∠AOB = 32° , m∠BOC = 50° 13. 8; m∠AOB = 30° , m∠BOC = 50° , m∠COD = 30° 14. 18; m∠AOB = 28° , m∠BOC = 52° , m∠AOD =108° 15. 7; m∠AOB = 31° , m∠BOC = 49° , m∠AOD =111°

Example 4 Name each angle in three ways. QExample …€¦ · 22. a straight angle, ^EFG 23. a...

Documents

Transcript of Example 4 Name each angle in three ways. QExample …€¦ · 22. a straight angle, ^EFG 23. a...