Section 7.4

Similarity in Right Triangles

Geometric Mean

•

The positive number of x such that

a x

═

x b

Similarity in Right Triangles

Find the geometric mean of 3 and 12.

Theorem

•

The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle to each other.

Case I

•

The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the length of the segments of the hypotenuse.

Examples

Case II

•

The altitude of the hypotenuse of a right triangle intersects it so that the length of each leg is the geometric mean of the length of its adjacent segment of the hypotenuse and the length of the entire hypotenuse.

Putting it all together

Solve for

x

and

y

.

Step it up - Example

•

Pg 395 #49

Homework

P394-395 2-20evens 21,34,36,50