1. Warm-up On a blank piece of paper compute the following perfect squares.. xx2x2 11 24 39 …… 20400

2. Agenda Start Chapter 8

3. Time for new

4. Radical, Dude 1.Thou shall not leave perfect squares under the radical! 2.Thou shall not leave partial perfect squares under the radical! 3.Thou shall not leave fractions under a radical! 4.Thou shall not leave radicals in the denominator!

5. Chapter 8 Geometric Mean – for any positive numbers a and b, the positive number x such that: b, x can not equal zero Cross Multiply – x 2 = ab extreme means Solve for x Example - Find the arithmetic and geometric mean between 2 and 10

6. Theorem 8-1 If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the two triangles formed are similar to the given triangle and to each other.

7. Theorem 8-2 The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.  ADC ~  CDB So  CD is the geometric mean of AD and BD

8. Theorem 8-3 If the altitude is drawn to the hypotenuse of a right triangle, then the measure of a leg of the triangle is the geometric mean between the measures of the hypotenuse and the segment of the hypotenuse adjacent to that leg.  NGT ~  NRT So  TG is the geometric mean of NT and RT

9. Examples

12. Theorem 8-4 Pythagorean Theorem In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. Given: rt.  ABC with rt.  at C Prove: a 2 + b 2 = c 2

13. Theorem 8-5 Converse of Pythagorean Theorem If the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle. 52 74 91 Right Triangle?

14. Examples

15. Answers Ahead

16. Radicals

19. 8-1 Study Guide

20. Homework 8-1 Study Guide