1. Splash Screen

2. Lesson Menu Objectives Vocabulary Example 1 Example 2 Example 3 Quick Quiz

3. Objectives To develop an understanding of how a right triangle and squares are related through the Pythagorean Theorem To use the Pythagorean Theorem to determine the missing side length or hypotenuse length of a right triangle To determine and use the distance formula To determine a graphical understanding of the Pythagorean Theorem

4. Vocabulary hypotenuse leg Pythagorean Theorem distance formula right triangle

5. Example 1 The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle. c 2 =a 2 + b 2 Pythagorean Theorem 25 2 =7 2 + 24 2 Replace a with 7, b with 24, and c with 25. ? ? 625=49 + 576Evaluate 25 2, 7 2, and 24 2. 625=625Simplify. Pythagorean Theorem

6. Example 1 Answer: The triangle is a right triangle. Pythagorean Theorem

7. 1.A 2.B 3.C Example 1 A.It is a right triangle. B.It is not a right triangle. C.not enough information to determine The measures of three sides of a triangle are 13 inches, 5 inches, and 12 inches. Determine whether the triangle is a right triangle.

8. Example 2 The cross-section of a camping tent is shown below. Find the width of the base of the tent. A.6 ft B.8 ft C.10 ft D.12 ft

9. Example 2 Read the Item From the diagram, you know that the tent forms two congruent right triangles. Let a represent half the base of the tent. Then w = 2a.

10. Example 2 Solve the Item c 2 =a 2 + b 2 Write the relationship. 10 2 =a 2 + 8 2 c = 10 and b = 8 100=a 2 + 64Evaluate 10 2 and 8 2. 100 – 64=a 2 + 64 – 64Subtract 64 from each side. 36=a 2 Simplify. Use the Pythagorean Theorem. =aDefinition of square root 6=aSimplify.

11. Example 2 The width of the base of the tent is 2a or (2)6 = 12 feet. Answer: Therefore, choice D is correct.

12. 1.A 2.B 3.C 4.D Example 2 A.15 ft B.18 ft C.20 ft D.22 ft This diagram shows the cross-section of a roof. How long is each rafter, r?

13. Example 3 Nikki kicks a ball from a position that is 2 yards behind the goal line and 4 yards from the side line (–2, 4). The ball lands 8 yards past the goal line and 2 yards from the same side line (8, 2). What distance, to the nearest tenth, was the ball kicked?

14. Example 3 d ≈ 10.2 Answer: 10.2 yards Distance Formula (x 1, y 1 ) = (–2, 4) (x 2, y 2 ) = (8, 2) Simplify. Evaluate powers. Simplify.

15. 1.A 2.B 3.C 4.D Example 3 A.0.2 mi B.0.5 mi C.2.2 mi D.5 mi MAPS The map of a college campus shows Gilmer Hall at (7, 3) and Watson House dormitory at (5, 4). If each unit on the map represents 0.1 mile, what is the distance between these buildings?

16. 1.A 2.B 3.C 4.D Quick Quiz 1 The sides of the right triangle are labeled. Find the hypotenuse. A.4 mm B.approximately 3.6 mm C.approximately 4.6 mm D.6 mm

17. 1.A 2.B 3.C 4.D Quick Quiz 2 If a triangle with squares attached have areas of 6 square units for the smallest square and 10 square units for the largest square, what is the missing area? A.8 square units B.16 square units C.4 square units D.12 square units

18. 1.A 2.B 3.C 4.D Quick Quiz 3 A right triangle has legs that measure 1 cm and 12 cm. What is the measure of the hypotenuse? A.21,025 cm B.145 cm C.approximately 11.8 cm D.approximately 12.04 cm

19. 1.A 2.B 3.C 4.D Quick Quiz 4 Hsin Lee wants to purchase a television that will fit into an entertainment center that has an opening of 30 inches by 40 inches. The size of a television is given in inches, and that number represents the diagonal of the screen. What is the largest television Hsin Lee can purchase? A.70 in. B.65 in. C.50 in. D.120 in.

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21. Resources Image Bank Math Tools Multilingual e-Glossary Rational Numbers Square RootsPythagorean Theorem

22. End of Custom Shows