Warm-up On a blank piece of paper compute the following perfect squares.. xx2x …… 20400

Agenda Start Chapter 8

Time for new

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!

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

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.

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

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

Examples

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

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 Right Triangle?

Examples

Answers Ahead

Radicals

8-1 Study Guide

Homework 8-1 Study Guide