Investigation: the Pythagorean Theorem

Name:______Assignment:______Investigation: The Pythagorean Theorem 1. The values in the chart represent the sides of a right triangle. Complete the chart.

Leg1 Leg2 Hyp (Leg1)2 (Leg2)2 (Leg1)2 + (Leg2)2 Hyp2 Hypotenuse 3 4 5 Leg 5 12 13 3 4 1 5 5 0.9 1.2 1.5 Leg

2. In a right triangle the side opposite the right angle is the longest side and also called the hypotenuse. Compare the legs and hypotenuse values above. Is our hypotenuse always the longest?

3. Compare the value of (Leg1)2 + (Leg2)2 for each row in the table to the value of Hyp2.

Name:______Assignment:______Investigation: The Pythagorean Theorem 1. The values in the chart represent the sides of a right triangle. Complete the chart.

Leg1 Leg2 Hyp (Leg1)2 (Leg2)2 (Leg1)2 + (Leg2)2 Hyp2 Hypotenuse 3 4 5 Leg 5 12 13 3 4 1 5 5 0.9 1.2 1.5 Leg

2. In a right triangle the side opposite the right angle is the longest side and also called the hypotenuse. Compare the legs and hypotenuse values above. Is our hypotenuse always the longest?

3. Compare the value of (Leg1)2 + (Leg2)2 for each row in the table to the value of Hyp2. 4. Complete the following statement: For a right triangle, the square of the longest side ______the sum of the squares of the other two sides.

5. The Pythagorean Theorem: In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. (Leg1)2 + (Leg2)2 = Hyp2

6. Determine whether the given lengths could be the sides of a right triangle. a. 9, 12, 15 b. 1, 2, 3

c. 2, 4, 5 d. 16, 30, 34

e. 4, 4, 8 f. 10, 24, 26

7. Find the length of the missing side. a. leg = 6, leg = 8 b. leg = 15, leg = 20

c. (be careful!) leg = 3, hyp = 5 d. leg = 5, hyp = 9

4. Complete the following statement: For a right triangle, the square of the longest side ______the sum of the squares of the other two sides.