Warmup On a blank piece of paper compute

Warm-up On a blank piece of paper compute the following perfect squares. . x 1 2 3 … 20 x 2 1 4 9 … 400

Agenda l Start Chapter 8

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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: Cross Multiply – x 2 extreme = ab means Solve for x b, x can not equal zero 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? 91 52 74

Examples

Answers Ahead

Radicals

8 -1 Study Guide

Homework l 8 -1 Study Guide