8-4 Similarity in Right Triangles One Key Term One Theorem Two Corollaries

Draw a diagonal across your index card. On one side of the card use a ruler to draw the altitude of the right triangle from the corner of the index card perpendicular to the diagonal. Cut out the three triangles, examine them

Theorem 8-3  Altitude Similarity Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. A C B D

Vocabulary 1. Geometric Mean 1.

#1 Finding the Geometric Mean  Find the geometric mean of 15 and 20.

1.The geometric mean can give a meaningful "average" to compare two companies. 2.The use of a geometric mean "normalizes" the ranges being averaged, so that no range dominates the weighting. 3.The geometric mean applies only to positive numbers. [2] [2] 4.It is also often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as data on the growth of the human population or interest rates of a financial investment.human population Purpose of the Geometric Mean

Corollary 1 to Theorem 8-3 The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse. A C B D

Corollary 2 to Theorem 8-3 The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse. A C B D

Similarity in Right Triangles Find the values of x and y in the following right triangle. 4 5 X Y Y X 4 + 5

You Try One!!! Find the values of x and y in the following right triangle.

#2 x 4 12 y Solve for x and y. 4x 12y x16 y