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7-2

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

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7-2

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

  2. 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.

  3. 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°

  4. Insert Lesson Title Here 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 30 21 18

  5. Are you remembering your skills? WARM-UP 5/6 1) 1 ½ + 2 ¾ = 4 1/4 2) 3 ½ - 2 2/3 = 9 1/3 1 5/16 3) 3 ½ x 2 2/3 = 4) 3 ½  2 2/3 = 5) 2.13 + 4.5 = 6.63 6) 5.13 - 4.5 = .63 7) 2.13 x 4.5 = 8) 2.4  .02 = 120 9.585 REVIEW TEST ON THESE THURSDAY

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

  7. A point is an exact location. P point 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. M 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. L N The building blocks of geometry are points, lines, and planes.

  8. Q P R M N PR and NR You can also write RP and RN. 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

  9. Point R is a point on PR and NR. Q P R M N 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.

  10. V U W T S UW and SW You can also write WU and WS. 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

  11. Point W is a point on WS and WU. V U W T S 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.

  12. 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 rayhas 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.

  13. B A C AB, BC, and AC You can also write BA, CB, and CA. AB, BC, and AC You can also write BA, CB, and CA. 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

  14. B AB, AC, BC, CB, CA, and BA A C AC 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.

  15. D E F DE, EF, and DF You can also write ED, FE, and FD. DE, EF, and DF You can also write ED, FE, and FD. 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

  16. D DE, EF, DF, FE, FD, and ED E F DF 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.

  17. 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

  18. What did the Acorn say when it grew up? Gee - I'm -a-tree! Geometry!

  19. Angles are everywhere!

  20. C AB, BA, and AC A B 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.

  21. SOME GEOMETRY JOKES

  22. Geometry & Measurement Chapter Five 5-1

  23. TODAY WE WILL... Learn to name, measure, classify, estimate, and draw angles. How do I use this thing?

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

  25. A Line A line extends in both directions for ever…never ending! A B AB

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

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

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

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

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

  31. 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

  32. 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.”

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

  34. What kind of angle is this? Right Angle!

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

  36. What kind of angle is this? Straight Angle!

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

  38. F H G 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.

  39. F H G 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.

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

  41. F H G • 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.

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

  43. What kind of angle is this? Obtuse Angle!

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

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

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

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

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

  49. What kind of angle is this? Acute Angle!

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