1. The Pythagorean Theorem Chapter 6

2. The Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

3. Converse of the Pythagorean Theorem If the lengths of the sides of a triangle satisfy the relationship a 2 +b 2 =c 2, where c is the hypotenuse, then the triangle is a right triangle.

4. Vocabulary The number 9 is called a perfect square since it is the square of the integer 3. The number 3 is called a square root of 9 because 3 2 =9. The symbol is called a radical sign. The radical sign indicates the positive square root of a number.  All positive numbers have two square roots.  Negative numbers do not have square roots.

8. 4 3

9. 7 24

10. 2 2

11. 4 8

12. A hot-air balloon is attached to a 75 foot rope that is tied to a post. A breeze blows the balloon to one side of the post, so that when the rope is taut the balloon is over the edge of a flower bed 21 feet from the post. How high above the flower bed is the balloon?

13. Homework