1. Apply the Pythagorean Theorem and Its Converse

2. Lesson Essential Question
Create one situation in which the Pythagorean Theorem or its converse is useful?

3. Terminology Hypotenuse – the side opposite the right angle
Pythagorean Theorem – the relationship between the lengths of the sides of a right triangle.

4. Example 1: Use the Pythagorean Theorem
Find the unknown length for the triangles:
a, b = 6, c = 7
A= 5, b = 12, c =

5. Ex 2: Use the Pythagorean Theorem
1) A right triangle has one leg that is 2 inches higher than the other leg. The length of the hypotenuse is √10 inches. Find the unknown lengths.
2) A right triangle has one leg that is 3 inches longer than the other leg. The length of the hypotenuse is 15 inches. Find the unknown lengths.

6. Ex 2: Continued
3) A right triangle has one leg that is 1 foot higher than the other leg. The length of the hypotenuse is √13 feet. Find the unknown lengths.

7. Ex 3: Application Problems
1) A soccer player makes a corner kick to another player, as shown. To the nearest yard, how far does the player kick the ball?
2) A rectangular pool is 30 feet wide and 60 feet long. You swim diagonally across the pool. To the nearest foot, how far do you swim?

8. Ex 4: Determine right triangles
Tell whether the triangles with the given side lengths is a right triangle.
1) 8, 15, 7 2) 5, 8, 9
3) 7, 23, 24 4) 5, 12, 13

9. Ex 5: Use the converse of the Pythagorean Theorem
1) A construction worker is making sure one corner of the foundation of the corner of a house is a right angle. To do this, the worker makes a mark 8 feet from the corner along one wall and another mark 6 feet from the same corner along the other wall. The worker then measures the distance between the two marks and finds the distance to be 10 feet. Is the corner a right angle?

10. Ex 5: Use the converse of the Pythagorean Theorem
2) A window has the shape of a triangle with the lengths of 120 centimeters, 120 centimeters, and 180 centimeters. Is the window a right triangle? Explain.

11. Summary Question
Create one situation in which the Pythagorean Theorem or its converse is useful?
Exchange this problem with a partner. Solve your partner’s problem.