2. Welcome to Interactive Chalkboard Pre-Algebra Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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4. Contents Lesson 10-1Line and Angle Relationships Lesson 10-2Congruent Triangles Lesson 10-3Transformations on the Coordinate Plane Lesson 10-4Quadrilaterals Lesson 10-5Area: Parallelograms, Triangles, and Trapezoids Lesson 10-6Polygons Lesson 10-7Circumference and Area: Circles Lesson 10-8Area: Irregular Figures

5. Lesson 1 Contents Example 1Find Measures of Angles Example 2Find a Missing Angle Measure Example 3Find Measures of Angles Example 4Apply Angle Relationships

6. Example 1-1a In the figure, m || n and t is a transversal. If find m  2 and m  8. Sinceare alternate exterior angles, they are congruent. So,. Sinceare corresponding angles, they are congruent. So,. Answer:

7. In the figure, m || n and t is a transversal. If find m  5 and m  1. Example 1-1b Answer:

8. Example 1-2a Read the Test Item Since are complementary,. Multiple-Choice Test Item If and  D and  E are complementary, what is m  E ? A 53° B 37° C 127° D 7°

9. Example 1-2a Solve the Test Item Complementary angles Replace with 53°. Subtract 53 from each side. Answer: The answer is B.

10. Example 1-2b Answer: A Multiple-Choice Test Item Ifand  G and  H are supplementary, what is m  h ? A 76° B 104° C 83° D 14°

11. Example 1-3a Angles PQR and STU are supplementary. If and, find the measure of each angle. Step 1 Find the value of x. Supplementary angles Substitution Combine like terms. Add 80 to each side. Divide each side by 2.

12. Example 1-3a Step 2Replace x with 130 to find the measure of each angle. Answer:

13. Angles ABC and DEF are complementary. If and, find the measure of each angle. Example 1-3b Answer:

14. Example 1-4a Transportation A road crosses railroad tracks at an angle as shown. Iffind m  6 and m  5. Sinceare corresponding angles, they are congruent. Answer: Sinceare supplementary angles, the sum of their measures is 180°. 180 – 131 = 49

15. Example 1-4b Transportation Main Street crosses Broadway Boulevard and Maple Avenue at an angle as shown. If m  1 = 48°, find m  3 and m  4. Answer:

16. End of Lesson 1

17. Lesson 2 Contents Example 1Name Corresponding Parts Example 2Use Congruence Statements Example 3Find Missing Measures

18. Example 2-1a Name the corresponding parts in the congruent triangles shown. Then complete the congruence statement. Answer:Corresponding Angles Corresponding Sides  HGI  ? One congruence statement is.

19. Example 2-1b Name the corresponding parts in the congruent triangles shown. Then complete the congruence statement. Answer:  ABC  ?

20. Example 2-2a If, complete each congruence statement. Explore You know the congruence statement. You need to find the corresponding parts. Plan Use the order of the vertices in to identify the corresponding parts. Solve

21. Example 2-2a Answer: M corresponds to Q, and N corresponds to P so N corresponds to P, and O corresponds to R so M corresponds to Q, and O corresponds to R so

22. Example 2-2a Examine Draw the triangles, using arcs and slash marks to show the congruent angles and sides.

23. If, complete each congruence statement. Example 2-2b Answer:

24. Example 2-3a  F and  C are corresponding angles. So, they are congruent. Since. Answer: Construction A brace is used to support a tabletop. In the figure,. What is the measure of  F ?

25. Example 2-3a Answer: What is the length of ? corresponds to. So,andare congruent. Since,.

26. Example 2-3b Art In the figure,. Answer: 44° a. What is the measure of  B ? b. What is the length of? Answer: 22 in.

27. End of Lesson 2

28. Lesson 3 Contents Example 1Translation in a Coordinate Plane Example 2Reflection in a Coordinate Plane Example 3Rotations in a Coordinate Plane

29. Example 3-1a The vertices of  ABC are A(–3, 7), B(–1, 0), and C(5, 5). Graph the triangle and the image of  ABC after a translation 4 units right and 5 units down. This translation can be written as the ordered pair (4, –5). To find the coordinates of the translated image, add 4 to each x -coordinate and add –5 to each y -coordinate. C(9, 0)  (4, –5)  C(5, 5) B(3, –5)  (4, –5)  B(–1, 0) A(1, 2)  (4, –5)  A(–3, 7) translation 4 right, 5 down vertex

30. Example 3-1a The coordinates of the vertices of  ABC are A(1, 2), B(3, –5), and C(9, 0). Graph  ABC and  ABC. Answer:

31. Example 3-1b The vertices of  DEF are D(–1, 5), E(–3, 1), and F(4, – 4). Graph the triangle and the image of  DEF after a translation 3 units left and 2 units up. Answer:

32. Example 3-2a The vertices of a figure are M(–8, 6), N(5, 9), O(2, 1), and P(–10, 3). Graph the figure and the image of the figure after a reflection over the y -axis. To find the coordinates of the vertices of the image after a reflection over the y -axis, multiply the x -coordinate by –1 and use the same y -coordinate. reflection vertex M(8, 6)  M(–8, 6) N(–5, 9)  N(5, 9) O(–2, 1)  O(2, 1) P(10, 3)  P(–10, 3)

33. Example 3-2a The coordinates of the vertices of the reflected figure are M(8, 6), N(–5, 9), O(–2, 1) and P(10, 3). Graph the figure and its image. Answer: –8–4 4 8 4

34. Example 3-2b The vertices of a figure are Q(–2, 4), R(–3, 1), S(3, –2), and T(4, 3). Graph the figure and the image of the figure after a reflection over the y -axis. Answer:

35. Example 3-3a A figure has vertices A(–4, 5), B(–2, 4), C(–1, 2), D(–3, 1), and E(–5, 3). Graph the figure and the image of the figure after a rotation of 180°. To rotate the figure, multiply both coordinates of each point by –1. E(5, –3)  E(–5, 3) D(3, –1)  D(–3, 1) C(1, –2)  C(–1, 2) B(2, –4)  B(–2, 4) A(4, –5)  A(–4, 5)

36. Example 3-3a The coordinates of the vertices of the rotated figure are A(4, –5), B(2, –4), C(1, –2), D(3, –1), and E(5, –3). Graph the figure and its image. Answer:

37. Example 3-3b A figure has vertices A(2, –1), B(3, 4), C(–3, 4), D(–5, –1), and E(1, –4). Graph the figure and the image of the figure after a rotation of 180°. Answer:

38. End of Lesson 3

39. Lesson 4 Contents Example 1Find Angle Measures Example 2Classify Quadrilaterals

40. Example 4-1a Find the value of x. Then find each missing angle measure. WordsThe sum of the measures of the angles is 360°. VariableLet m  Q, m  R, m  S, and m  T represent the measures of the angles.

41. Answer: The value of x is 35. So, and. Example 4-1a Equation Angles of a quadrilateral Substitution Combine like terms. Subtract 185 from each side. Simplify. Divide each side by 5.

42. Example 4-1b Find the value of x. Then find each missing angle measure. Answer:

43. Example 4-2a Classify the quadrilateral using the name that best describes it. Answer: It is a trapezoid. The quadrilateral has one pair of opposite sides parallel.

44. Example 4-2a Classify the quadrilateral using the name that best describes it. Answer: It is a parallelogram. The quadrilateral has both pairs of opposite sides parallel and congruent.

45. Example 4-2a Classify the quadrilateral using the name that best describes it. Answer: It is a square. The quadrilateral has four congruent sides and four right angles.

46. Example 4-2b Answer: rectangleAnswer: trapezoid Classify each quadrilateral using the name that best describes it. a.b. c. Answer: parallelogram

47. End of Lesson 4

48. Lesson 5 Contents Example 1Find Areas of Parallelograms Example 2Find Areas of Triangles Example 3Find Area of a Trapezoid Example 4Use Area to Solve a Problem

49. Example 5-1a Find the area of the parallelogram. The base is 3 meters. The height is 3 meters. Area of a parallelogram Replace b with 3 and h with 3. Multiply. Answer: The area is 9 square meters.

50. Example 5-1a Find the area of the parallelogram. The base is 4.3 inches. The height is 6.2 inches. Area of a parallelogram Replace b with 4.3 and h with 6.2. Multiply. Answer: The area is 26.66 square inches.

51. Answer: 1.95 ft 2 Example 5-1b Find the area of each parallelogram. Answer: 12 cm 2 a.b.

52. Example 5-2a Find the area of the triangle. The base is 3 meters. The height is 4 meters. Area of a triangle Replace b with 3 and h with 4. Answer: The area of the triangle is 6 square meters. Multiply.

53. Example 5-2a Find the area of the triangle. The base is 3.9 feet. The height is 6.4 feet. Area of a triangle Replace b with 3.9 and h with 6.4.

54. Example 5-2a Answer: The area of the triangle is 12.48 square feet. Multiply.

55. Example 5-2b Find the area of each triangle. a.b. Answer:

56. Example 5-3a Find the area of the trapezoid. Area of a trapezoid The height is 6 meters. The bases aremeters and meters. Replace h with 6 and a with and b with.

57. Example 5-3a Divide out the common factors. Simplify. Answer: The area of the trapezoid is square meters.

58. Example 5-3b Find the area of the trapezoid. Answer:

59. Example 5-4a Painting A wall that needs to be painted is 16 feet wide and 9 feet tall. There is a doorway that is 3 feet by 8 feet and a window that is 6 feet by feet. What is the area to be painted? To find the area to be painted, subtract the areas of the door and window from the area of the entire wall.

60. Example 5-4a Area of the wallArea of the doorArea of the window Answer: The area to be painted is 144 – 24 – 33 or 87 square feet.

61. Example 5-4b Gardening A garden needs to be covered with fresh soil. The garden is 12 feet wide and 15 feet long. A rectangular concrete path runs through the middle of the garden and is 3 feet wide and 15 feet long. Find the area of the garden which needs to be covered with fresh soil. Answer:

62. End of Lesson 5

63. Lesson 6 Contents Example 1Classify Polygons Example 2Measures of Interior Angles Example 3Find Angle Measure of a Regular Polygon

64. Example 6-1a Classify the polygon. This polygon has 5 sides. Answer: It is a pentagon.

65. Example 6-1a Classify the polygon. This polygon has 7 sides. Answer: It is a heptagon.

66. Example 6-1b Classify each polygon. Answer: heptagonAnswer: hexagon a.b.

67. Example 6-2a Find the sum of the measures of the interior angles of a quadrilateral. A quadrilateral has 4 sides. Therefore,. Replace n with 4. Simplify. Answer: The sum of the measures of the interior angles of a quadrilateral is 360°.

68. Example 6-2b Find the sum of the measures of the interior angles of a pentagon. Answer: 540°

69. Example 6-3a Traffic Signs A stop sign is a regular octagon. What is the measure of one interior angle in a stop sign? Step 1 Find the sum of the measures of the angles. An octagon has 8 sides. Therefore,. Replace n with 8. Simplify. Step 2 Divide the sum by 8 to find the measure of one angle. The sum of the measures of the interior angles is 1080°. Answer: So, the measure of one interior angle in a stop sign is 135°.

70. Example 6-3b Picnic Table A picnic table in the park is a regular hexagon. What is the measure of one interior angle in the picnic table? Answer: 120°

71. End of Lesson 6

72. Lesson 7 Contents Example 1Find the Circumference of a Circle Example 2Use Circumference to Solve a Problem Example 3Find Areas of Circles

73. Answer: The circumference is about 37.7 meters. Example 7-1a Find the circumference of the circle to the nearest tenth. Circumference of a circle Replace d with 12. Simplify. This is the exact circumference. To estimate the circumference, use a calculator. ENTER 2nd [  ] 37.69911184 12

74. Example 7-1a Find the circumference of the circle to the nearest tenth. Circumference of a circle Replace r with 7.1. Simplify. Use a calculator. Answer: The circumference is about 44.6 meters.

75. Example 7-1b Answer: 10.1 cmAnswer: 12.6 ft Find the circumference of each circle to the nearest tenth. a.b.

76. Example 7-2a Landscaping A landscaper has a tree whose roots form a ball-shaped bulb with a circumference of about 110 inches. How wide will the landscaper have to dig the hole in order to plant the tree? Explore You know the circumference of the roots of the tree. You need to know the diameter of the hole to be dug. Plan Use the formula for the circumference of a circle to find the diameter. Solve Circumference of a circle Replace C with 110. Divide each side by .

77. Example 7-2a Answer: The diameter of the hole should be at least 35 inches. The solution is reasonable. Examine Check the reasonableness of the solution by replacing d with 35 in. Circumference of a circle Replace d with 35. Simplify. Use a calculator.

78. Example 7-2b Swimming Pool A circular swimming pool has a circumference of 24 feet. Matt must swim across the diameter of the pool. How far will Matt swim? Answer: about 7.6 ft

79. Example 7-3a Find the area of the circle. Round to the nearest tenth. Area of a circle Replace r with 11. Evaluate. Use a calculator. Answer: The area is about 380.1 square feet.

80. Example 7-3a Find the area of the circle. Round to the nearest tenth. Replace r with 4.15. Use a calculator. Answer: The area is about 54.1 square centimeters. Area of a circle Evaluate.

81. Example 7-3b Answer: Find the area of each circle. Round to the nearest tenth. b.a.

82. End of Lesson 7

83. Lesson 8 Contents Example 1Find Area of Irregular Figures Example 2Use Area of Irregular Figures

84. Example 8-1a Find the area of the figure to the nearest tenth. Explore You know the dimensions of the figure. You need to find its area. Plan Solve a simpler problem. First, separate the figure into a triangle, square, and a quarter-circle. Then find the sum of the areas of the figure.

85. Example 8-1a Find the area of the figure to the nearest tenth. Solve Area of Triangle Area of a triangle Replace b with 2 and h with 4. Simplify.

86. Example 8-1a Find the area of the figure to the nearest tenth. Solve Area of Square Area of a square Replace b and h with 2. Simplify.

87. Example 8-1a Find the area of the figure to the nearest tenth. Solve Area of Quarter-circle Area of a quarter-circle Replace r with 2. Simplify. Answer: The area of the figure is or about 11.1 square inches.

88. Example 8-1b Find the area of the figure to the nearest tenth. Answer:

89. Example 8-2a Carpeting Carpeting costs $2 per square foot. How much will it cost to carpet the area shown? Step 1Find the area to be carpeted. Area of Rectangle Area of a rectangle Replace b with 14 and h with 10. Simplify.

90. Example 8-2a Carpeting Carpeting costs $2 per square foot. How much will it cost to carpet the area shown? Area of Square Area of a square Replace b and h with 3. Simplify.

91. Example 8-2a Carpeting Carpeting costs $2 per square foot. How much will it cost to carpet the area shown? Area of Triangle Replace b with 14 and h with 12. Simplify. The area to be carpeted is or 233 square feet. Area of a triangle

92. Example 8-2a Carpeting Carpeting costs $2 per square foot. How much will it cost to carpet the area shown? Step 2Find the cost of the carpeting. Answer:So, it will cost $466 to carpet the area shown.

93. Example 8-2b Painting One gallon of paint is advertised to cover 100 square feet of wall surface. About how many gallons will be needed to paint the wall shown below? Answer: about 4 gallons

94. End of Lesson 8

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