1. Pythagorean Theorem and it’s Converse

2. Pythagorean Theorem Pythagorean Theorem: used for right triangles, it is a tool used to solve for a missing side of a right triangle a, b  are the legs of the triangle c  must by the hypotenuse (the longest side of the triangle)

3. Examples… Find the missing side of the triangle. 1. 2. The side missing is c because it is the side across from the right angle. 10 is c because it is across from the right angle. That means you are missing one of the legs (a).

4. You try… Find the length of the missing side. 1. 2. 3.4.

5. Answers and Solutions… 1.2. 3.4.

6. Application of Pythagorean Theorem 1.The foot of a ladder is placed 12 feet from a wall. If the top of the ladder rests 16 feet up on the wall, how long is the ladder? 2.David’s TV screen is 10 inches long. If the diagonal measures 25 inches, how long is the width of David's TV?

7. Converse of Pythagorean Theorem Used to determine if 3 measurements create a right triangle. If 3 measurements form a right triangle, then… *because c must be the hypotenuse, the longest side given will always be used as c Determine if the following triangles are right triangles. 1.2. True statement, so YES a right triangle. False statement, so NO, not a right triangle.

8. You try… Determine whether the following triangles are right triangles. 1.2.

9. Answers and Solutions… 1.2.

10. Pythagorean Triple A set of positive integers that form a right triangle… Most well known triples: 3, 4, 5 5, 12, 13 7, 24, 25 8, 15, 17 9, 40, 41

11. What type of triangle is it? Pythagorean Theorem can also be used to determine what type of triangle 3 measurements make.

12. What type of triangle is it? Determine what type of triangle is given. 1.2.3.

13. You try… Determine whether each triangle is acute, right, or obtuse. 1.2. 3.4.

14. Answers and Solutions… 1. 2. 3. 4.