Chapter 7 Section 4 Similarity in Right

Triangles

Objectives Students will be able to find and use

relationships within right triangles

Essential Understanding When you draw the altitude to the

hypotenuse of a right triangle you form three pairs of similar triangles

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.

What similarity statement can you write relating the three triangles?

Geometric Mean Proportions in which the means are

equal For numbers a and b, the geometric

mean is the positive number x such that:

a = xx b

Then you cross multiply and solve for x

Find the Geometric Mean Geometric mean of 6 and 15 Geometric mean of 4 and 18 Geometric mean of 5 and 12

From the first example

Theorem The length of an altitude to the

hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

Theorem 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 hypotenuses and the length of the segment of the hypotenuses adjacent to the leg

Example

What are the values of x and y?

What are the values of x and y?

What are the values of x and y?

Homework Pg. 465 # 9 – 23, 31, 38 – 41 20 problems