1. Geometry Notes Lesson 5.1B Pythagorean Theorem T.2.G.4 Apply the Pythagorean Theorem and its converse in solving practical problems

2. Pythagorean Theorem In a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. a (leg) b (leg) c (hypotenuse)

3. Example 1: Solve for x. Leave your answer in simplest radical form. x 8 20

4. Example 2: Solve for x. Leave your answer in simplest radical form. in. 3 in. x

5. Example 3: Solve for x. Leave your answer in simplest radical form. x 1213 1.Use the Pythagorean Theorem to find the third side of the left-side triangle. 2.Now you can use the Pythagorean Theorem again to find x on the right-side triangle.

6. Converse of the Pythagorean Theorem If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

7. Converse of the Pythagorean Theorem The Converse of the Pythagorean Theorem leads to the inequalities below: In triangle ABC with longest side c, We also know that... If, then the triangle is obtuse. If, then the triangle is acute. If, then the triangle is right.

8. Example 4: If a triangle has sides of 20, 21, and 28 cm, is it acute, obtuse, or right? Longest side? Then…

9. Problem Solving with the Pythagorean Theorem A 15 foot ladder is leaning against a building. The base of the ladder is 5 feet from the building. To the nearest foot, how high up the building does the ladder reach? 1. Draw a picture and label the sides of the right triangle. 2. Use the Pythagorean Theorem to find the missing side.