2. 7-2 Angles Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

3. Problem of the Day Draw a clock face that includes the numerals 1–12. Draw two lines that do not intersect and that separate the clock face into three parts so that the sums of the numbers on each part are the same.

4. Problem of the Day The measure of Jack’s angle is twice that of Amy’s and half that of Nate’s. The sum of the measures of Amy’s and Trisha’s angles is equal to the sum of the measures of Jack’s and Nate’s angles. The sum of the measures of all the angles is equal to 180°. What is the measure of each student’s angle? Jack’s angle: 30°; Nate’s angle: 60°; Amy’s angle: 15°; Trisha’s angle: 75°

5. MORE WARM-UP Use the following data set: 18, 20, 56, 47, 30, 18, 21. 1. Find the range.2. Find the mean. 3. Find the median.4. Find the mode. 38 Insert Lesson Title Here 30 21 18

6. Are you remembering your skills? 1) 1 ½ + 2 ¾ =2) 3 ½ - 2 2/3 = 3) 3 ½ x 2 2/3 = 4) 3 ½  2 2/3 = 5) 2.13 + 4.5 =6) 5.13 - 4.5 = 7) 2.13 x 4.5 = 8) 2.4 .02 = 4 1/4 5/6 9 1/31 5/16 6.63.63 9.585 120 REVIEW TEST ON THESE THURSDAY

7. LETS GO BACK TO 4 th grade for a moment

8. The building blocks of geometry are points, lines, and planes. A plane is a flat surface that plane LMN, extends without end in all plane MLN, directions. plane NLM A plane is named by three points on the plane that are not on the same line. M N L A point is an exact location. Ppoint P, P A point is named by a capital letter. A line is a straight path that line AB, AB, extends without end in A B line BA, BA opposite directions. A line is named by two points on the line.

9. Additional Example 1A &1B: Identifying Points, Lines, and Planes Use the diagram to name each geometric figure. A. three points M, N, and P Five points are labeled: points M, N, P, Q, and R. B. two lines PR and NR You can also write RP and RN. Q N P RM

10. Additional Example 1C & 1D: Identifying Points, Lines, and Planes Use the diagram to name each geometric figure. C. a point shared by two lines point R D. a plane plane QRM Use any three points in the plane that are not on the same line. Write the three points in any order. Point R is a point on PR and NR. Q N P RM

11. Try This: Example 1A &1B Use the diagram to name each geometric figure. A. three points S, T, and U Five points are labeled: points S, T, U, V, and W. B. two lines UW and SW You can also write WU and WS. V S U W T

12. Try This: Example 1C & 1D Use the diagram to name each geometric figure. C. a point shared by two lines point W D. a plane plane VUT Use any three points in the plane that are not on the same line. Write the three points in any order. Point W is a point on WS and WU. V S U W T

13. A line segment is a line segment XY, XY, made of two endpoints Y line segment YX, YX and all the points between X the endpoints. A line segment is named by its endpoints. A ray has one endpoint. ray JK, JK From the endpoint, the ray J K extends without end in one direction only. A ray is named by its endpoint first followed by another point on the ray.

14. Additional Example 2A & 2B: Identifying Line Segments and Rays Use the diagram to give a possible name to each figure. A. three different line segments B. three ways to name the line You can also write BA, CB, and CA. AB, BC, and AC You can also write BA, CB, and CA. AB, BC, and AC C A B

15. Additional Example 2C & 2D: Identifying Line Segments and Rays Use the diagram to give a possible name to each figure. C. six different rays D. another name for ray AB A is still the endpoint. C is another point on the ray. AB, AC, BC, CB, CA, and BA AC C A B

16. Try This: Example 2A & 2B Use the diagram to give a possible name to each figure. A. three different line segments B. three ways to name the line You can also write ED, FE, and FD. DE, EF, and DF You can also write ED, FE, and FD. DE, EF, and DF F D E

17. Try This: Example 2C & 2D Use the diagram to give a possible name to each figure. C. six different rays D. another name for ray DE D is still the endpoint. F is another point on the ray. DE, EF, DF, FE, FD, and ED DF F D E

18. CAN YOU ANSWER THESE??? What geometry term might you associate with each object? 1. a string on a guitar 2. a window 3. the tip of a pencil 4. a sheet of paper line segment plane or rectangle point plane or rectangle

19. What did the Acorn say when it grew up?

21. Segerson’s Warm Up 1. Draw two points. Label one point A and the other point B. 2. Draw a line through points A and B. 3. Draw a ray with A as an endpoint and C as a point on the ray. 4. Name all the rays in your drawing. AB, BA, and AC AB C

22. SOME GEOMETRY JOKES

24. Geometry & Measurement Chapter Five 5-1

25. Learn to name, measure, classify, estimate, and draw angles. How do I use this thing?

26. Vocabulary angle vertex acute angle right angle obtuse angle straight angle Insert Lesson Title Here

27. A Line A line extends in both directions for ever…never ending! AB ABAB

28. A Ray A ray has one endpoint and extends without end in one direction.

29. Ray identification A ray is named by its endpoint and one other point on the ray. AB A B

30. An Angle An angle is two rays with a common endpoint

31. Vertex A vertex is the common endpoint of two rays

32. Angle Identification An angle is identified by the three points…the vertex is in the middle! A B C ABC Written like this! CBA or B

33. Angle Measurement An angle is measured by degrees and can be classified according to their measures. Acute Angle Right Angle Obtuse Angle Straight Angle less than 90º is 90º more than 90º is exactly 180º

34. An angle is formed by two rays with a common endpoint, called the vertex. An angle can be named by its vertex or by its vertex and a point from each ray. The middle point in the name should always be the vertex. Angles are measured in degrees. The number of degrees determines the type of angle. Use the symbol ° to show degrees: 90° means “90 degrees.”

35. An acute angle measures less than 90°. A right angle measures exactly 90°.

36. What kind of angle is this?

37. An obtuse angle measures more than 90° and less than 180°. A straight angle measures exactly 180°.

38. What kind of angle is this?

39. Warm Up Simplify. 1.x + 7 = 180 2. 18 + x = 90 3. 180 = x + 43 4.90= x + 47 x = 173 x = 72 x = 137 x = 43 Solving Subtraction Equations

40. Additional Example 1: Measuring an Angle with a Protractor Use a protractor to measure the angle. Tell what type of angle it is. Place the center point of the protractor on the vertex of the angle. G H F

41. Additional Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. Place the protractor so that ray GH passes through the 0° mark. G H F

42. Using the scale that starts with 0° along ray GH, read the measure where ray GF crosses. Additional Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. G H F

43. The measure of FGH is 120°. Write this as m FGH = 120°. Additional Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. G H F

44. Since 120° > 90° and 120° < 180°, the angle is obtuse. Additional Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. G H F

45. What kind of angle is this?

46. Try This: Example 1 Use a protractor to measure the angle. Tell what type of angle it is. H I G Place the center point of the protractor on the vertex of the angle.

47. Try This: Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. Place the protractor so that ray HI passes through the 0° mark. H I G

48. Try This: Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. H I G Using the scale that starts with 0° along ray HI, read the measure where ray HI crosses.

49. Try This: Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. H I G The measure of GHI is 70°. Write this as m GHI = 70°.

50. Try This: Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. H I G Since 70° < 90°, the angle is acute.

51. What kind of angle is this?

52. Additional Example 2: Drawing an Angle with a Protractor Use a protractor to draw an angle that measures 80°. Draw a ray on a sheet of paper.

53. Additional Example 2 Continued Use a protractor to draw an angle that measures 80°. Place the center point of the protractor on the endpoint of the ray. Place the protractor so that the ray passes through the 0° mark.

54. Additional Example 2 Continued Use a protractor to draw an angle that measures 80°. Make a mark at 80° above the scale on the protractor. Use a straightedge to draw a ray from the endpoint of the first ray through the mark you make at 80°.

55. Try This: Example 2 Use a protractor to draw an angle that measures 45°. Draw a ray on a sheet of paper.

56. Place the center point of the protractor on the endpoint of the ray. Place the protractor so that the ray passes through the 0° mark. Try This: Example 2 Continued Use a protractor to draw an angle that measures 45°.

57. Make a mark at 45° above the scale on the protractor. Use a straightedge to draw a ray from the endpoint of the first ray through the mark you make at 45°. Try This: Example 2 Continued Use a protractor to draw an angle that measures 45°.

58. To estimate the measure of an angle, compare it with an angle whose measure you already know. A right angle has half the measure of a straight angle. A 45° angle has half the measure of a right angle.

59. Now, let’s go to 6 th grade!

60. WARM UP Draw a 45 degree angle without a protractor Draw a 135 degree angle without a protractor Draw a 10 degree angle without a protractor THEN, check to see if you were correct by using a protractor

61. Additional Example 3: Estimating Angle Measures Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate.

62. Let’s take a commercial break Can think about what they can see Can think about what they can’t see

63. That is what this was all about!

66. At first glance, tell me what you see! Do you see a vase? Or do you see something more. Look Closely!!!!

67. Additional Example 3: Estimating Angle Measures Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate.

68. Additional Example 3: Estimating Angle Measures Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate.

69. Additional Example 3: Estimating Angle Measures Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate.

70. Additional Example 3: Estimating Angle Measures Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate. 90° About half of 90° 90 plus 45 = 135

71. So….. Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate. Think: The measure of the angle is about halfway between 90° and 180°. A good estimate would be 135°. The angle measures 131°, so the estimate is reasonable.

72. CAN YOU SEE THIS ONE? Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate. Think: The measure of the angle is a little more than halfway between 0° and 90°. A good estimate would be 50°. The angle measures 52°, so the estimate is reasonable.

73. How about this one 45 About 20-25

74. How about this one About 165- 170 or so

75. How about this one 85 or so?

76. Warm-up Use a protractor to draw an angle with the given measure. Tell what type of angle it is. 1. 130° 2. 26° 3. Draw a right angle. 4. Is the angle shown closer to 30° or 120°? acute obtuse Insert Lesson Title Here 30°

78. Protractor A protractor is used to measure angles in degrees…º 140º

79. Protractor Place the Vertex of the angle in the middle…. 220º

80. Protractor How do you know which number to use…220º or 40º? 220º An obtuse angle!

83. Protractor A right angle! 90º

84. Protractor An Acute angle! 45º

85. Congruent If two angles have the same measure, they are congruent 40º Ã Ã

86. “Congruent” means… “The same measure”

87. Find Congruent Angles!