1. Over Lesson 10–4 5-Minute Check 1

2. Over Lesson 10–4 5-Minute Check 2

3. Splash Screen The Pythagorean Theorem and Distance Formula Lesson 10-5

4. Then/Now Understand how to solve problems using the Pythagorean Theorem and determine whether a triangle is a right triangle. Understand how to use the Distance Formula to find the distance between two points.

5. Vocabulary

6. Concept 1

7. Example 1A Find the Length of a Side A. Find the length of the missing side. If necessary, round to the nearest hundredth. Answer: 30 units c 2 = a 2 + b 2 Pythagorean Theorem c 2 = 18 2 + 24 2 a = 18 and b = 24 c 2 = 324 + 576Evaluate squares. c 2 = 900Simplify. Use the positive value. c Take the square root of each side.

8. Example 1B Find the Length of a Side B. Find the length of the missing side. If necessary, round to the nearest hundredth. c 2 = a 2 + b 2 Pythagorean Theorem 16 2 = 9 2 + b 2 a = 9 and c = 16 256 = 81 + b 2 Evaluate squares. 175 = b 2 Subtract 81 from each side. Answer: about 13.23 units Take the square root of each side. 13.23 ≈ b

9. Example 1A A. Find the length of the hypotenuse of a right triangle if a = 25 and b = 60.

10. Example 1B B. Find the length of the missing side.

11. Example 2 Find the Length of a Side TELEVISION The diagonal of a television screen is 32 inches. The width of the screen is 21 inches. Find the height of the screen. 32 2 = h 2 + 21 2 Pythagorean Theorem 1024 = h 2 + 441Evaluate squares. 583 = h 2 Subtract 441 from each side. Answer: The screen is approximately 24.15 inches high. Use the positive value. Take the square root of each side.

12. Example 2 HIKING Amarita is hiking out directly east from her camp on the plains. She walks for 6 miles before turning right and walking 7 more miles towards the south. After her hiking, how far does she need to walk for the shortest route straight back to camp?

13. Concept 2 If a triangle is a right triangle, then the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. The converse can be used to determine whether a triangle is a right triangle. Converse of the Pythagorean Theorem

14. Example 3 Check for Right Triangles Determine whether 7, 12, and 15 can be the lengths of the sides of a right triangle. Since the measure of the longest side is 15, let c = 15, a = 7, and b = 12. Then determine whether c 2 = a 2 + b 2. Answer: Since c 2 ≠ a 2 + b 2, the triangle is not a right triangle. 225= 49 + 144Evaluate squares. ? ? 15 2 = 7 2 + 12 2 a = 7, b = 12, and c = 15 225≠ 193Add. c 2 = a 2 + b 2 Pythagorean Theorem

15. Example 3 Determine whether 33, 44, and 55 can be the lengths of the sides of a right triangle.

16. Pythagorean Triple

20. End of the Lesson Homework Page 650 #11-43(odd); 46-47; Page 654 #1-13 odd