2. CHAPTER OUTLINE 8 Measurement and Geometry Slide 2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 8.1U.S. Customary Units of Measurement 8.2Metric Units of Measurement 8.3Converting Between U.S. Customary and Metric Units 8.4Medical Applications Involving Measurement 8.5Lines and Angles 8.6Triangles and the Pythagorean Theorem

3. CHAPTER OUTLINE 8 Measurement and Geometry Slide 3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 8.7Perimeter, Circumference, and Area 8.8Volume and Surface Area

4. Section Objectives 8.1 U.S. Customary Units of Measurement Slide 4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.U.S. Customary Units 2.U.S. Customary Units of Length 3.Units of Time 4.U.S. Customary Units of Weight 5.U.S. Customary Units of Capacity

5. Section 8.1 U.S. Customary Units of Measurement 1.U.S. Customary Units Slide 5 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. To measure an object means to assign it a number and a unit of measure.

6. Section 8.1 U.S. Customary Units of Measurement 1.U.S. Customary Units (continued) Slide 6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Summary of U.S. Customary Units of Length, Time, Weight, and Capacity

7. Section 8.1 U.S. Customary Units of Measurement 1.U.S. Customary Units Slide 7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

8. Section 8.1 U.S. Customary Units of Measurement 2.U.S. Customary Units of Length Slide 8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. A conversion factor is a ratio of equivalent measures. In a unit ratio, the quotient is 1 because we are dividing measurements of equal length. To convert from one unit of measure to another, we can multiply by a unit ratio.

9. PROCEDUREChoosing a Unit Ratio as a Conversion Factor Slide 9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. In a unit ratio, The unit of measure in the numerator should be the new unit you want to convert to. The unit of measure in the denominator should be the original unit you want to convert from.

10. Example 1Converting Units of Length by Using Unit Ratios Slide 10 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Convert the units of length.

11. Example Solution: 1Converting Units of Length by Using Unit Ratios Slide 11 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. From the table, we have 1 yd = 3 ft. Notice that the original units of ft reduce or “cancel” in much the same way as simplifying fractions. The unit yd remains in the final answer.

12. Example Solution: 1Converting Units of Length by Using Unit Ratios (continued) Slide 12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. b. From the table, we have 1 mi = 1760 yd.

13. Example Solution: 1Converting Units of Length by Using Unit Ratios Slide 13 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. c. From the table we have 1 mi = 5280 ft.

14. Example 2Making Multiple Conversions of Length Slide 14 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

15. Example Solution: 2Making Multiple Conversions of Length Slide 15 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. To convert miles to inches, we use two conversion factors. The first unit ratio converts miles to feet. The second unit ratio converts feet to inches.

16. Example Solution: 2Making Multiple Conversions of Length Slide 16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

17. Example 3Adding and Subtracting Mixed Units of Measurement Slide 17 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

18. Example Solution: 3Adding and Subtracting Mixed Units of Measurement (continued) Slide 18 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

19. Example Solution: 3Adding and Subtracting Mixed Units of Measurement Slide 19 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

20. Example 5Converting Units of Time Slide 20 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. After running a marathon, Dave crossed the finish line and noticed that the race clock read 2:20:30. Convert this time to minutes.

21. Example Solution: 5Converting Units of Time Slide 21 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The notation 2:20:30 means 2 hr 20 min 30 sec. We must convert 2 hr to minutes and 30 sec to minutes. Then we add the total number of minutes. The total number of minutes is 120 min + 20 min + 0.5 min. Dave finished the race in 140.5 min.

22. Section 8.1 U.S. Customary Units of Measurement 4.U.S. Customary Units of Weight Slide 22 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Measurements of weight record the force of an object subject to gravity.

23. Example 6Converting Units of Weight Slide 23 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. The average weight of an adult male African elephant is 12,400 lb. Convert this value to tons. b. Convert the weight of a 7-lb 3-oz baby to ounces.

24. Example Solution: 6Converting Units of Weight (continued) Slide 24 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. Recall that 1 ton = 2000 lb. An adult male African elephant weighs 6.2 tons.

25. Example Solution: 6Converting Units of Weight Slide 25 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

26. Example 7Applying U.S. Customary Units of Weight Slide 26 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Jessica lifts four boxes of books. The boxes have the following weights: 16 lb 4 oz, 18 lb 8 oz, 12 lb 5 oz, and 22 lb 9 oz. How much weight did she lift altogether?

27. Example Solution: 7Applying U.S. Customary Units of Weight Slide 27 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

28. Section 8.1 U.S. Customary Units of Measurement 5.U.S. Customary Units of Capacity Slide 28 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Capacity is the volume or amount that a container can hold. The U.S. Customary units of capacity are fluid ounces (fl oz), cup (c), pint (pt), quart (qt), and gallon (gal).

29. Example 8Converting Units of Capacity Slide 29 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Convert the units of capacity.

30. Example Solution: 8Converting Units of Capacity (continued) Slide 30 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

31. Example Solution: 8Converting Units of Capacity Slide 31 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

32. Example A recipe calls for c of chicken broth. A can of chicken broth holds 14.5 fl oz. Is there enough chicken broth in the can for the recipe? 9Applying Units of Capacity Slide 32 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

33. Example Solution: 9Applying Units of Capacity Slide 33 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. We need to convert each measurement to the same unit of measure for comparison. The recipe calls for c or 14 fl oz of chicken broth. The can of chicken broth holds 14.5 fl oz, which is enough.

34. Section Objectives 8.2 Metric Units of Measurement Slide 34 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Introduction to the Metric System 2.Metric Units of Length 3.Metric Units of Mass 4.Metric Units of Capacity 5.Summary of Metric Conversions

35. Section 8.2 Metric Units of Measurement 1.Introduction to the Metric System Slide 35 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The metric system, a simple, decimal-based system of units, is the predominant system of measurement used in science. The simplicity of the metric system is a result of having one basic unit of measure for each type of quantity (length, mass, and capacity). The base units are the meter for length, the gram for mass, and the liter for capacity. Other units of length, mass, and capacity in the metric system are products of the base unit and a power of 10.

36. Section 8.2 Metric Units of Measurement 2.Metric Units of Length Slide 36 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The meter (m) is the basic unit of length in the metric system. A meter is slightly longer than a yard.

37. Section 8.2 Metric Units of Measurement 2.Metric Units of Length Slide 37 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Metric Units of Length and Their Equivalents

38. Section 8.2 Metric Units of Measurement 2.Metric Units of Length Slide 38 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

39. Example 1Measuring Distances in Metric Units Slide 39 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Approximate the distance in centimeters and in millimeters.

40. Example Solution: 1Measuring Distances in Metric Units Slide 40 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The numbered lines on the ruler are units of centimeters. Each centimeter is divided into 10 mm. We see that the width of the penny is not quite 2 cm. We can approximate this distance as 1.8 cm or equivalently 18 mm.

41. Example 2Converting Metric Units of Length Slide 41 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

42. Example Solution: 2Converting Metric Units of Length Slide 42 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. From the table, 1 km = 1000 m.

43. Section 8.2 Metric Units of Measurement 2.Metric Units of Length Slide 43 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The place positions in our numbering system are based on powers of 10. For this reason, when we multiply a number by 10, 100, or 1000, we move the decimal point 1, 2, or 3 places, respectively, to the right. Similarly, when we multiply by 0.1, 0.01, or 0.001, we move the decimal point to the left 1, 2, or 3 places, respectively. Since the metric system is also based on powers of 10, we can convert between two metric units of length by moving the decimal point.

44. Section 8.2 Metric Units of Measurement 2.Metric Units of Length Slide 44 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

45. PROCEDUREUsing the Prefix Line to Convert Metric Units Slide 45 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Step 1 To use the prefix line, begin at the point on the line corresponding to the original unit you are given. Step 2 Then count the number of positions you need to move to reach the new unit of measurement. Step 3 Move the decimal point in the original measured value the same direction and same number of places as on the prefix line. Step 4 Replace the original unit with the new unit of measure.

46. Example 3Using the Prefix Line to Convert Metric Units of Length Slide 46 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

47. Example Solution: 3Using the Prefix Line to Convert Metric Units of Length Slide 47 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

48. Section 8.2 Metric Units of Measurement 3.Metric Units of Mass Slide 48 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The fundamental unit of mass in the metric system is the gram (g).

49. Section 8.2 Metric Units of Measurement 3.Metric Units of Mass Slide 49 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Metric Units of Mass and Their Equivalents

50. Section 8.2 Metric Units of Measurement 3.Metric Units of Mass Slide 50 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

51. Example 4Converting Metric Units of Mass Slide 51 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

52. Example Solution: 4Converting Metric Units of Mass (continued) Slide 52 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

53. Example Solution: 4Converting Metric Units of Mass Slide 53 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

54. Section 8.2 Metric Units of Measurement 4.Metric Units of Capacity Slide 54 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The basic unit of capacity in the metric system is the liter (L).

55. Section 8.2 Metric Units of Measurement 4.Metric Units of Capacity Slide 55 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Metric Units of Capacity and Their Equivalents

56. Section 8.2 Metric Units of Measurement 4.Metric Units of Capacity Slide 56 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

57. Section 8.2 Metric Units of Measurement 4.Metric Units of Capacity Slide 57 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 mL is also equivalent to a cubic centimeter (cc or cm 3 ). The unit cc is often used to measure dosages of medicine.

58. Example 5Converting Metric Units of Capacity Slide 58 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

59. Example Solution: 5Converting Metric Units of Capacity (continued) Slide 59 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

60. Example Solution: 5Converting Metric Units of Capacity Slide 60 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

61. Section 8.2 Metric Units of Measurement 5.Summary of Metric Conversions Slide 61 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

62. Example 7Converting Metric Units Slide 62 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. The distance between San Jose and Santa Clara is 26 km. Convert this to meters. b. A bottle of canola oil holds 946 mL. Convert this to liters. c. The mass of a bag of rice is 90,700 cg. Convert this to grams. d. A dose of an antiviral medicine is 0.5 cc. Convert this to milliliters.

63. Example Solution: 7Converting Metric Units Slide 63 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

64. Section Objectives 8.3 Converting Between U.S. Customary and Metric Units Slide 64 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Summary of U.S. Customary and Metric Unit Equivalents 2.Converting U.S. Customary and Metric Units 3.Applications 4.Units of Temperature

65. Example 1Converting Metric Units to U.S. Customary Units Slide 65 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

66. Example Solution: 1Converting Metric Units to U.S. Customary Units Slide 66 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

67. Section 8.3 Converting Between U.S. Customary and Metric Units 1.Summary of U.S. Customary and Metric Unit Equivalents Slide 67 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

68. Example 2Converting Units of Length Slide 68 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Fill in the blank. Round to two decimal places, if necessary.

69. Example Solution: 2Converting Units of Length (continued) Slide 69 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

70. Example Solution: 2Converting Units of Length Slide 70 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

71. Example 3Converting Units of Weight and Mass Slide 71 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

72. Example Solution: 3Converting Units of Weight and Mass Slide 72 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

73. Example 4Converting Units of Capacity Slide 73 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

74. Example Solution: 4Converting Units of Capacity Slide 74 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

75. Example 5Converting Units in an Application Slide 75 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. A 2-L bottle of soda sells for $2.19. A 32-oz bottle of soda sells for $1.59. Compare the price per quart of each bottle to determine the better buy.

76. Example Solution: 5Converting Units in an Application (continued) Slide 76 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Note that 1 qt = 2 pt = 4 c = 32 fl oz. So a 32-oz bottle of soda costs $1.59 per quart. Next, if we can convert 2 L to quarts, we can compute the unit cost per quart and compare the results.

77. Example Solution: 5Converting Units in an Application Slide 77 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Now find the cost per quart. The cost for the 2-L bottle is $1.04 per quart, whereas the cost for 32 oz is $1.59 per quart. Therefore, the 2-L bottle is the better buy.

78. Section 8.3 Converting Between U.S. Customary and Metric Units 4.Units of Temperature Slide 78 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

79. Section 8.3 Converting Between U.S. Customary and Metric Units 4.Units of Temperature Slide 79 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

80. Slide 80 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FORMULA Conversions for Temperature Scale

81. Example 7Converting Units of Temperature Slide 81 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

82. Example Solution: 7Converting Units of Temperature Slide 82 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

83. Example 8Converting Units of Temperature Slide 83 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

84. Example Solution: 8Converting Units of Temperature Slide 84 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

85. Section Objectives 8.4 Medical Applications Involving Measurement Slide 85 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Additional Metric Units of Mass 2.Medical Applications

86. Section 8.4 Medical Applications Involving Measurement 1.Additional Metric Units of Mass Slide 86 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sometimes doctors prescribe medicines in very small amounts. In these cases, it is sometimes more convenient to use units of micrograms. The abbreviation for microgram is mcg or sometimes g.

87. Example 1Converting Units of Micrograms Slide 87 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. Convert. b. A doctor gives a heart patient an initial dose of 200 mcg of nitroglycerin. How many milligrams is this?

88. Example Solution: 1Converting Units of Micrograms Slide 88 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

89. Example 2Applying Metric Units of Measure to Medicine Slide 89 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. A doctor orders the antibiotic oxacillin for a child. The dosage is 12.5 mg of the drug per kilogram of the child’s body mass. This dosage is given 4 times a day. a. How much of the drug should a 24-kg child get in one dose? b. How much of the drug would the child get if she were on a 10-day course of the antibiotic?

90. Example Solution: 2Applying Metric Units of Measure to Medicine Slide 90 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. We need to multiply the unit rate of 12.5 mg per kilogram times the child’s body mass. b. For a 10-day course, we need to multiply 300 g by the number of doses per day (4), and the total number of days (10).

91. Section Objectives 8.5 Lines and Angles Slide 91 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Basic Definitions 2.Naming and Measuring Angles 3.Complementary and Supplementary Angles 4.Parallel and Perpendicular Lines

92. Section 8.5 Lines and Angles 1.Basic Definitions Slide 92 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

93. Example 1Identifying Points, Lines, Line Segments, and Rays Slide 93 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

94. Example Solution: 1Identifying Points, Lines, Line Segments, and Rays Slide 94 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

95. Section 8.5 Lines and Angles 2.Naming and Measuring Angles Slide 95 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. An angle is a geometric figure formed by two rays that share a common endpoint. The common endpoint is called the vertex of the angle.

96. Section 8.5 Lines and Angles 2.Naming and Measuring Angles Slide 96 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The most common unit to measure an angle is the degree, denoted by.

97. Section 8.5 Lines and Angles 2.Naming and Measuring Angles Slide 97 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Approximate the measure of an angle by using a tool called a protractor.

98. Section 8.5 Lines and Angles 2.Naming and Measuring Angles Slide 98 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

99. Example 2Measuring Angles Slide 99 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Read the protractor to determine the measure of each angle.

100. Example 2Measuring Angles Slide 100 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

101. Example Solution: 2Measuring Angles Slide 101 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

102. Section 8.5 Lines and Angles 2.Naming and Measuring Angles Slide 102 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

103. Section 8.5 Lines and Angles 3.Complementary and Supplementary Angles Slide 103 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

104. Example 3Identifying Supplementary and Complementary Angles Slide 104 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

105. Example Solution: 3Identifying Supplementary and Complementary Angles Slide 105 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

106. Section 8.5 Lines and Angles 4.Parallel and Perpendicular Lines Slide 106 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

107. Section 8.5 Lines and Angles 4.Parallel and Perpendicular Lines Slide 107 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Angles that share a side are called adjacent angles.

108. Section 8.5 Lines and Angles 4.Parallel and Perpendicular Lines Slide 108 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. If two lines intersect at a right angle, they are perpendicular lines.

109. Section 8.5 Lines and Angles 4.Parallel and Perpendicular Lines Slide 109 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Lines L 1 and L 2 are parallel lines. If a third line m intersects the two parallel lines, eight angles are formed.

110. Section 8.5 Lines and Angles 4.Parallel and Perpendicular Lines (continued) Slide 110 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

111. Section 8.5 Lines and Angles 4.Parallel and Perpendicular Lines (continued) Slide 111 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

112. Section 8.5 Lines and Angles 4.Parallel and Perpendicular Lines Slide 112 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

113. Example 1Finding the Measure of Angles in a Diagram Slide 113 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Assume that lines L 1 and L 2 are parallel. Find the measure of each angle, and explain how the angle is related to the given angle of 65

114. Example Solution: 1Finding the Measure of Angles in a Diagram Slide 114 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

115. Section Objectives 8.6 Triangles and the Pythagorean Theorem Slide 115 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Triangles 2.Square Roots 3.Pythagorean Theorem

116. PROPERTYAngles of a Triangle Slide 116 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

117. Example 1Finding the Measure of Angles Within a Triangle Slide 117 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

118. Example Solution: 1Finding the Measure of Angles Within a Triangle (continued) Slide 118 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

119. Example Solution: 1Finding the Measure of Angles Within a Triangle Slide 119 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

120. Section 8.6 Triangles and the Pythagorean Theorem 1.Triangles Slide 120 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

121. Section 8.6 Triangles and the Pythagorean Theorem 1.Triangles Slide 121 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

122. TIP: Slide 122 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sometimes we use tick marks to denote segments of equal length. Similarly, we sometimes use a small arc to denote angles of equal measure.

123. Example 2Evaluating Squares and Square Roots Slide 123 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

124. Example Solution: 2Evaluating Squares and Square Roots Slide 124 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

125. Section 8.6 Triangles and the Pythagorean Theorem 3.Pythagorean Theorem Slide 125 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

126. PROPERTYPythagorean Theorem Slide 126 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. For any right triangle, Using the letters a, b, and c to represent the legs and hypotenuse, respectively, we have

127. Example 3Finding the Length of the Hypotenuse of a Right Triangle Slide 127 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Find the length of the hypotenuse of the right triangle.

128. Example Solution: 3Finding the Length of the Hypotenuse of a Right Triangle (continued) Slide 128 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The lengths of the legs are given. Label the triangle, using a, b, and c. It does not matter which leg is labeled a and which is labeled b. Apply the Pythagorean theorem. Substitute a = 6 and b = 8. Simplify.

129. Example Solution: 3Finding the Length of the Hypotenuse of a Right Triangle Slide 129 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The solution to this equation is the positive number, c, that when squared equals 100. Simplify the square root of 100. The solution may be checked using the Pythagorean theorem.

130. Example 4Finding the Length of a Leg in a Right Triangle Slide 130 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Find the length of the unknown side of the right triangle.

131. Example Solution: 4Finding the Length of a Leg in a Right Triangle Slide 131 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The solution may be checked by using the Pythagorean theorem.

132. Example 5Using the Pythagorean Theorem in an Application Slide 132 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. When Barb swam across a river, the current carried her 300 yd downstream from her starting point. If the river is 400 yd wide, how far did Barb swim?

133. Example Solution: 5Using the Pythagorean Theorem in an Application (continued) Slide 133 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. We first familiarize ourselves with the problem and draw a diagram. The distance Barb actually swims is the hypotenuse of the right triangle. Therefore, we label this distance c.

134. Example Solution: 5Using the Pythagorean Theorem in an Application Slide 134 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

135. Section Objectives 8.7 Perimeter, Circumference, and Area Slide 135 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Quadrilaterals 2.Perimeter and Circumference 3.Area

136. Section 8.7 Perimeter, Circumference, and Area 1.Quadrilaterals (continued) Slide 136 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Recall that a polygon is a flat figure formed by line segments connected at their ends. A four-sided polygon is called a quadrilateral.

137. Section 8.7 Perimeter, Circumference, and Area 1.Quadrilaterals Slide 137 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

138. Section 8.7 Perimeter, Circumference, and Area 2.Perimeter and Circumference Slide 138 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Recall that the perimeter of a polygon is the distance around the figure. Also recall that the “perimeter” of a circle is called the circumference.

139. Slide 139 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FORMULA Perimeter and Circumference

140. Example 1Finding Perimeter and Circumference Slide 140 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

141. Example Solution: 1Finding Perimeter and Circumference (continued) Slide 141 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

142. Example Solution: 1Finding Perimeter and Circumference (continued) Slide 142 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

143. Example Solution: 1Finding Perimeter and Circumference Slide 143 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

144. Section 8.7 Perimeter, Circumference, and Area 3.Area Slide 144 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Recall that the area of a region is the number of square units that can be enclosed within the region.

145. (continued) Slide 145 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FORMULA Area Formulas

146. Slide 146 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FORMULA Area Formulas

147. Example 2Finding Area (continued) Slide 147 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

148. Example 2Finding Area Slide 148 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

149. Example Solution: 2Finding Area (continued) Slide 149 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. The field is in the shape of a parallelogram. The base is 0.6 km and the height is 1.8 km. The field is 1.08 km 2.

150. Example Solution: 2Finding Area Slide 150 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. b. To find the area of the matting only, we can subtract the inner area from the outer 8-in. by 10-in. area. In each case, apply the formula, A = lw. The matting is 32 in. 2

151. Example 3Finding Area Slide 151 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

152. Example Solution: 3Finding Area (continued) Slide 152 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

153. Example Solution: 3Finding Area (continued) Slide 153 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

154. Example Solution: 3Finding Area Slide 154 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

155. Example 4Computing the Area of a Circle Slide 155 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

156. Example Solution: 4Computing the Area of a Circle (continued) Slide 156 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

157. Example Solution: 4Computing the Area of a Circle Slide 157 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

158. Example 5Finding Area for a Landscaping Application Slide 158 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sod can be purchased in palettes for $225. If a palette contains 240 ft 2 of sod, how much will it cost to cover the area in the figure?

159. Example Solution: 5Finding Area for a Landscaping Application (continued) Slide 159 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. To find the total cost, we need to know the total number of square feet. Then we can determine how many 240-ft 2 palettes are required.

160. Example Solution: 5Finding Area for a Landscaping Application (continued) Slide 160 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

161. Example Solution: 5Finding Area for a Landscaping Application Slide 161 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. To determine how many 240-ft 2 palettes of sod are required, divide the total area by 240 ft 2. Number of palettes: The total cost for 20 palettes is The cost for the sod is $4500.

162. Section Objectives 8.8 Volume and Surface Area Slide 162 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Volume 2.Surface Area

163. Section 8.8 Volume and Surface Area 1.Volume Slide 163 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Volume is another word for capacity. Volume can be measured in cubic units.

164. Slide 164 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FORMULA Notice that the volume formulas for these three figures are given by the product of the area of the base and the height of the figure:

165. Slide 165 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FORMULA

166. Example 1Finding Volume Slide 166 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Find the volume. Round to the nearest whole unit.

167. Example Solution: 1Finding Volume (continued) Slide 167 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

168. Example Solution: 1Finding Volume Slide 168 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. We can visualize the volume by “layering” cubes that are each 1 in. high. The number of cubes in each layer is equal to 4 3 = 12. Each layer has 12 cubes, and there are 5 layers. Thus, the total number of cubes is 12 5 = 60 for a volume of 60 in 3.

169. Example 2Finding the Volume of a Cylinder Slide 169 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

170. Example Solution: 2Finding the Volume of a Cylinder Slide 170 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

171. Example 3Finding the Volume of a Sphere Slide 171 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

172. Example Solution: 3Finding the Volume of a Sphere (continued) Slide 172 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

173. Example Solution: 3Finding the Volume of a Sphere (continued) Slide 173 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

174. Example 4Finding the Volume of a Cone Slide 174 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

175. Example Solution: 4Finding the Volume of a Cone Slide 175 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

176. Section 8.8 Volume and Surface Area 2.Surface Area Slide 176 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Surface area (often abbreviated SA) is the area of the surface of a three-dimensional object.

177. Section 8.8 Volume and Surface Area 2.Surface Area Slide 177 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

178. Example 5Determining Surface Area Slide 178 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Determine the surface area of the rectangular solid.

179. Example Solution: 5Determining Surface Area Slide 179 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

180. Example 6Determining Surface Area Slide 180 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

181. Example Solution: 6Determining Surface Area Slide 181 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.