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4. Contents Lesson 13-1Angles Lesson 13-2Using Angle Measures Lesson 13-3Bisectors Lesson 13-4Two-Dimensional Figures Lesson 13-5Lines of Symmetry Lesson 13-6Similar and Congruent Figures

5. Lesson 1 Contents Example 1Measure Angles Example 2Measure Angles Example 3Find Missing Angle Measures

6. Example 1-1a Use a protractor to find the measure of the angle. Then classify the angle as acute, obtuse, right, or straight. Answer: The angle measures It is an acute angle.

7. Example 1-1b Use a protractor to find the measure of the angle. Then classify the angle as acute, obtuse, right, or straight. Answer: obtuse

8. Example 1-2a Use a protractor to find the measure of the angle. Then classify the angle as acute, obtuse, right, or straight. Answer: The angle measures It is an obtuse angle.

9. Example 1-2b Use a protractor to find the measure of the angle. Then classify the angle as acute, obtuse, right, or straight. Answer: obtuse

10. Complementary angles Example 1-3a ALGEBRA Angles P and Q are complementary. Subtract from each side. Answer: the answer is correct.

11. Example 1-3b Answer: ALGEBRA Angles A and B are complementary.

12. End of Lesson 1

13. Lesson 2 Contents Example 1Estimate Angle Measures Example 2Draw an Angle

14. Example 2-1a Estimate the measure of the angle shown. Answer: about Compare the given angle to an angle whose measure you know. The angle is greater than and less than. So, a reasonable estimate is about

15. Example 2-1b Estimate the measure of the angle shown. Sample answer: about 65 

16. Example 2-2a Draw a angle. Step 1 Draw one side of the angle. Then mark the vertex and draw an arrow. Step 2 Place the center point of the protractor on the vertex. Align the mark labeled 0 on the protractor with the line. Find on the correct scale and make a pencil mark.

17. Example 2-2b Step 3 Use a straightedge to draw the side that connects the vertex and the pencil mark. Answer:

18. Example 2-2c Draw a angle. Answer:

19. End of Lesson 2

20. Lesson 3 Contents Example 1Bisect a Line Segment Example 2Bisect an Angle

21. Example 3-1a Use a straightedge and a compass to bisect Step 1 Draw

22. Example 3-1b Step 2 Place the compass at point P. Using a setting greater than one half the length of draw two arcs.

23. Example 3-1c Step 3 Using the same setting, place the compass at point Q. Draw an arc above and below.

24. Example 3-1d Step 4 Use a straightedge to align the intersections. Draw a segment that intersects Label the intersection M. Answer:

25. Example 3-1e Use a straightedge and a compass to bisect Answer:

26. Example 3-2a Use a straightedge and a compass to bisect Step 1 Draw

27. Example 3-2b Step 2 Place the compass at point E and draw an arc that intersects both sides of the angle. Label the points of intersection X and Y.

28. Example 3-2c Step 3 With the compass at point X, draw an arc.

29. Example 3-2d Step 4 Using the same setting, place the compass point at Y and draw another arc. Label the intersection Z.

30. Example 3-2e Step 5 Use a straightedge to draw Answer: Therefore, are congruent. This can be written as

31. Example 3-2f Use a straightedge and a compass to bisect Answer:

32. End of Lesson 3

33. Lesson 4 Contents Example 1Identify a Polygon Example 2Analyze Two-Dimensional Figures

34. Example 4-1a Identify the polygon. Then tell whether it is a regular polygon. Answer: The polygon has 7 sides. So, it is a heptagon. Since the sides and angles are congruent, it is a regular polygon.

35. Example 4-1b Identify the polygon. Then tell whether it is a regular polygon. Answer: octagon; regular

36. Example 4-2a STAMPS Depending on the design, some U.S. postal stamps are in the shape of a square, while others are rectangular. Identify and then describe the similarities and differences between a square and a rectangle. Answer: These shapes are alike because they both have four sides, opposite sides parallel, opposite sides congruent, and four right angles. These shapes are different because a square has four congruent sides and a rectangle does not necessarily have four congruent sides.

37. Example 4-2b QUILTING When making a quilt, Edna uses pieces of fabric shaped as squares and rhombuses. Identify and describe the similarities and differences between a square and a rhombus. Answer: similarities–four sides, all sides congruent, opposite sides parallel; differences–A square has four right angles and a rhombus does not have any right angles.

38. End of Lesson 4

39. Lesson 5 Contents Example 1Draw Lines of Symmetry Example 2Draw Lines of Symmetry Example 3Draw Lines of Symmetry Example 4Identify Line Symmetry Example 5Identify Rotational Symmetry Example 6Identify Rotational Symmetry

40. Example 5-1a Draw all lines of symmetry for the figure. This figure has 1 line of symmetry. Answer:

41. Example 5-1b Draw all lines of symmetry for the figure. Answer:

42. Example 5-2a Draw all lines of symmetry for the figure. Answer: The figure has no lines of symmetry.

43. Example 5-2b Draw all lines of symmetry for the figure. Answer: none

44. Example 5-3a Draw all lines of symmetry for the figure. The figure has 4 lines of symmetry. Answer:

45. Example 5-3b Draw all lines of symmetry for the figure. Answer:

46. Example 5-4a MULTIPLE- CHOICE TEST ITEM A star from a car company’s logo is shown. How many lines of symmetry does this star have? A 1 B 2 C 5 D none Read the Test Item You need to find all of the lines of symmetry for the star.

47. Example 5-4b Solve the Test Item Draw all lines of symmetry. It is a good idea to number each line so that you do not count a line twice. There are 5 lines of symmetry. Answer: C

48. Example 5-4c MULTIPLE- CHOICE TEST ITEM A triangle appears in an advertisement for a new restaurant. How many lines of symmetry does the triangle have? A none B 1 C 2 D 3 Answer: D

49. Example 5-5a Tell whether the figure has rotational symmetry. Answer: So, the figure has rotational symmetry. When the figure is rotated the figure looks as it did before it was rotated.

50. Example 5-5b Tell whether the figure has rotational symmetry. Answer: yes

51. Example 5-6a Tell whether the figure has rotational symmetry. Answer: So, the figure does not have rotational symmetry. The figure appears as it did before being rotated only after being rotated 360 .

52. Example 5-6b Tell whether the figure has rotational symmetry. Answer: no

53. End of Lesson 5

54. Lesson 6 Contents Example 1Identify Similar and Congruent Figures Example 2Identify Similar and Congruent Figures Example 3Apply Similarity and Congruence Example 4Apply Similarity and Congruence

55. Example 6-1a Tell whether the pair of figures is similar, congruent, or neither. Answer: They are similar. The figures have the same shape but not the same size.

56. Example 6-1b Tell whether the pair of figures is similar, congruent, or neither. Answer: neither

57. Example 6-2a Tell whether the pair of figures is similar, congruent, or neither. Answer: The figures have neither the same shape nor size.

58. Example 6-2b Tell whether the pair of figures is similar, congruent, or neither. Answer: similar

59. Example 6-3a SKATEBOARDING RAMPS The two ramps shown are congruent. What side of corresponds with side Answer: Side corresponds to side

60. Example 6-3b Answer: FLOOR TILES The two floor tiles shown are congruent. What side of rectangle ABCD corresponds with side on rectangle EFGH?

61. Example 6-4a Answer: The perimeter of is 24 feet. SKATEBOARDING RAMPS The two ramps shown are congruent. What is the perimeter of The perimeter of Since the triangles are congruent, they have the same size and shape.

62. Example 6-4b Answer: 40 in. FLOOR TILES The two floor tiles shown are congruent. What is the perimeter of rectangle ABCD?

63. End of Lesson 6

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