6-3 The Pythagorean Theorem Pythagorean Theorem

a2 + b2 = c2

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

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

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)

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

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

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

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

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 = ?

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