Geometric Mean & the Pythagorean Thm. Section 7-1 & 7-2.

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Presentation transcript:

Geometric Mean & the Pythagorean Thm. Section 7-1 & 7-2

The geometric mean between 2 positive numbers a and b is the positive number x where x 2 = ab x =

Thm. 7-1 If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the 2 triangles formed are similar to the given triangle and to each other.

A B D C

Thm. 7-2 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 2 segments of the hypotenuse.

a h b

Thm. 7-3 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.

d h e a b c

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. a b c a 2 + b 2 = c 2 Converse is also true.

Pythagorean Triples If the measures of a right triangle are whole numbers, the measures of the sides are a Pythagorean triple

Joke Time What is a twip? A twip is what a wabbit takes when he wides on a twain.

What is gray, has big ears and has a trunk? A mouse going on vacation