2. Example 1-3a ALGEBRA Solve Write the equation. Take the square root of each side. The equation has two solutions, Answer: Notice that

3. Example 1-3b Answer: ALGEBRA Solve

4. Splash Screen

5. Ch. 3-4 The Pythagorean Theorem

6. Vocabulary Pythagorean Theorem: describes the relationship between the lengths of the legs and the hypotenuse for any right triangle C² = a² + b² a c b Hypotenuse: the side opposite the right angle. It is the longest side of the triangle. Legs

7. Example 4-1a KITES Find the length of the kite string. The kite string forms the hypotenuse of a right triangle. The vertical and horizontal distances form the legs. Pythagorean Theorem c = 13 Answer: The string of the kite is 13 ft.

8. Example 4-1b KITES Find the length of the kite string. Answer: 26 ft

9. Example 4-2a The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. Find the length of the other leg. Pythagorean Theorem Replace c with 33 and b with 28. Subtract 784 from each side. Simplify. Take the square root of each side. Answer: The length of the other leg is about 17.5 cm.

10. Example 4-2b The hypotenuse of a right triangle is 26 centimeters long and one of its legs is 17 centimeters. Find the length of the other leg. Answer: about 19.7 cm

11. Example 4-3a MULTIPLE–CHOICE TEST ITEM A 10–foot ramp is extended from the back of a truck to the ground to help movers load furniture onto the truck. If the ramp touches the ground at a point 9 feet behind the truck, how high off the ground is the top of the ramp? A about 1 foot B about 4.4 feet C about 13.5 feet D about 19 feet

12. Example 4-3a Read the Test Item You know the length of the ramp and the distance from the truck to the bottom of the ramp. Make a drawing of the situation including the right triangle.

13. Example 4-3a Answer: B The top of the ramp is about 4.4 feet off the ground. Pythagorean Theorem Replace c with 10 and b with 9. Subtract 81 from each side. Simplify. Take the square root of each side. Simplify. Evaluate Solve the Test Item

14. Example 4-3b MULTIPLE–CHOICE TEST ITEM The base of a 12–foot ladder is 5 feet from the wall. How high can the ladder reach? A about 7 feet B about 10.9 feet C about 11.8 feet D about 13 feet Answer: B

15. Example 4-4a The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle. Answer: The triangle is a right triangle. Pythagorean Theorem Simplify. Replace a with 7, b with 24, and c with 25. Evaluate

16. Example 4-4b The measures of three sides of a triangle are 13 inches, 5 inches, and 12 inches. Determine whether the triangle is a right triangle. Answer: yes

17. Ch.3-5 Distance on the Coordinate Plane

18. Example 6-1a Graph the ordered pairs (0, –6) and (5, –1). Then find the distance between the points. Let the distance between the two points,, a b c c² = a² + b² c² = 5² + 5² c² = 25 + 25 c² = 50 c = √50 ≈ 7.07 Answer: The points are about 7.1 units apart.

19. Example 6-1b Graph the ordered pairs (0, –3) and (2, –6). Then find the distance between the points. Answer: about 3.6 units

20. Example 6-2a TRAVEL Melissa lives in Chicago. A unit on the grid of her map shown below is 0.08 mile. Find the distance between McCormickville at (–2, –1) and Lake Shore Park at (2, 2). Let the distance between McCormickville and Lake Shore Park. Then a = 3 and b = 4.

21. Example 6-2a Pythagorean Theorem Answer: Since each unit equals 0.08 mile, the distance is 0.08  5 = 0.4 mile. The distance between McCormickville and Lake Shore Park is 5 units on the map. Replace a with 3 and b with 4. Take the square root of each side.

22. Example 6-2b TRAVEL Sato lives in Chicago. A unit on the grid of his map shown below is 0.08 mile. Find the distance between Shantytown at (2, –1) and the intersection of N. Wabash Ave. and E. Superior St. at (–1, 1). Answer: 0.4 mile

23. Ch. 3-3 The Real Number System

24. Integers: …,-2,-1,0, 1,2,… Whole numbers: 0,1,2,3,… Natural Numbers: 1,2,3,… Rational numbers: has terminated decimal or repeating decimal. E.g. 1/6 =0.1666… or 1/8 = 0.125 Irrational numbers: no terminated decimal or repeating decimal. E.g. √2 = 1.4142135… Real numbers: rational numbers + irrational numbers. So, all numbers are real numbers.

25. Example 3-1a Name all sets of numbers to which belongs. Answer: Since it is a whole number, an integer, and a rational number.

26. Example 3-1b Answer: whole, integer, rational Name all sets of numbers to which belongs.

27. Example 3-2a Answer: Since the decimal does not repeat or terminate, it is an irrational number. Name all sets of numbers to which belongs. …

28. Example 3-2b Answer: irrational Name all sets of numbers to which belongs.

29. Example 3-3a Name all sets of numbers to which 0.090909… belongs. The decimal ends in a repeating pattern. Answer: It is a rational number because it is equivalent to

30. Example 3-3b Name all sets of numbers to which 0.1010101010… belongs. Answer: rational

31. 5-Minute Check

32. Online Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Mathematics: Applications and Concepts, Course 3 Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to www.msmath3.net/extra_examples.

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