1. 6-3
The Pythagorean Theorem
Pythagorean Theorem

2. a2 + b2 = c2

3. Find the Length of a Hypotenuse
Additional Example 1A:
Find the Length of a Hypotenuse
Find the length of the hypotenuse. c A. 4 5

4. Find the length of the hypotenuse.
Try This: Example 1A
Find the length of the hypotenuse. c A. 5 7

5. Find the length of the hypotenuse.
Try This: Example 1B
Find the length of the hypotenuse.
B. triangle with coordinates (–2, –2), (–2, 4), and (3, –2) x y
(–2, 4)
(–2, –2)
(3, –2)

6. Finding the Length of a Leg in a Right Triangle
Additional Example: 2
Finding the Length of a Leg in a Right Triangle
Solve for the unknown side in the right triangle. 25 b 7

7. Try This: Example 2 Solve for the unknown side in the right triangle.12 b 4

8. Using the Pythagorean Theorem to Find Area
Additional Example 3:
Using the Pythagorean Theorem to Find Area
Use the Pythagorean Theorem to find the height of the triangle. Then use the height to find the area of the triangle. 6 6 a 4 4

9. Try This: Example 3
Use the Pythagorean Theorem to find the height of the triangle. Then use the height to find the area of the triangle. 5 5 a 2 2

10. Using the Pythagorean Theorem
Additional Example 3:
Using the Pythagorean Theorem
Use the Pythagorean Theorem to find each missing measure.
a = ? b = 24 c = 26
a = 13 b = 18 c = ?

11. Using the Pythagorean Theorem
Additional Example 3:
Using the Pythagorean Theorem
Determine whether each triangle is a right triangle.
a = 3 b = 4 c = 5