7.4 Similarity in Right Triangles
Theorem 7.3 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 C B D A
Vocabulary Geometric mean - the number x such that , where a, b and x are positive numbers
Example Find the geometric mean of 4 and 18
Try it Find the geometric mean of 3 and 48
Corollary 1 to Theorem 7.3 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
Corollary 2 to Theorem 7.3 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
Solve for x and y x y 5 4
Answer Use Corollary 2 to solve for x Use corollary 1 to solve for y
Solve for x and y 4 x 12 y
Answer Use Corollary 2 to solve for x Use corollary 1 to solve for y
Classwork/Homework Pgs 394-395 #2-22 even, 26-36 even