1. Lesson 9.3 – 9.4 The Pythagorean Theorem Essential Question: How do you use the Pythagorean theorem to solve problems?

2. Before we start…

3. What are the parts of the right triangle? The hypotenuse is the side opposite the right angle. It is the longest side of the right triangle. The legs are the two sides that form the right angle.

4. What is the Pythagorean theorem? It states the relationship among the lengths of the sides of a right triangle. A theorem is a statement that can be proved true.

5. What does the Pythagorean theorem say? If a triangle is a right triangle, then the sum of the squares of the lengths of the legs equals the square of the lengths of the hypotenuse.

6. How do you use the Pythagorean theorem to solve problems?

7. Find the unknown length for the triangle shown.

11. Find the length of the hypotenuse of a right triangle with a 15 inch leg and a 20 inch leg.

12. Find the length of the hypotenuse of a right triangle with a 28 inch leg and a 45 inch leg.

13. What is the Converse of the Pythagorean Theorem?

14. How do you use the converse of the Pythagorean theorem?

15. Tell whether the triangle with the given side lengths is a right triangle. 8, 15, 17

16. Tell whether the triangle with the given side lengths is a right triangle. 5, 8, 9

17. Tell whether the triangle with the given side lengths is a right triangle. 7, 23, 24

18. Tell whether the triangle with the given side lengths is a right triangle. 5, 12, 13

19. A soccer player makes a corner kick to another player, as shown. To the nearest yard, how far does the player kick the ball?

20. You and your friend live on different sides of a lake. To ride your bicycle to your friend’s house, you travel 0.5 mile directly east, and then 1.2 miles directly south. How far is it to your friend’s house by boat?

21. To get to town from the park office your travel 4 miles directly east, then 9 miles directly north. How far is town in a straight line “as the crow flies?” Round your answer to the nearest hundredth of a mile.

22. What is the diagonal length of a TV screen whose dimensions are 80 centimeters by 60 centimeters?

23. Find the perimeter and area of the triangle.

26. What is a Pythagorean triple?

27. Do these sides form a Pythagorean triple?

31. How do you use the Pythagorean theorem to solve problems?

32. Ticket Out the Door Find the missing side length in the right triangle.