Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 a x 2 x = ab x = ab x b 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. C A D B ADC ~ CDB 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. h a b a h 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. a h d c a a d b e c c b b e 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. c 2 2 2 a a +b =c b 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. 3-4-5 5-12-13 8-15-17 7-24-25 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