WARM UP: Are triangle KRA and triangle FLN similar? How do you know?

A flagpole casts a shadow 18 ft. long. At the same time, Rachael casts a shadow that is 4 ft. long. If Rachel is 5 ft. tall, what is the height of the flagpole?

Are the triangles similar? If so, what is the similarity statement.

7.4 - Similarity in Right Triangles

I can find and use relationships in similar right triangles.

When you draw the altitude to the hypotenuse of a right triangle, you form three pairs of right

triangles.

Theorem 7 – 3

Theorem If… Then…

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.

Triangle ABC is a right triangle with right <ACB, and CD is the altitude

to the hypotenuse…

Problem Identifying Similar Triangles

What similarity statement can you write relating the three triangles in the diagram?

Problem: Identifying Similar Triangles

What similarity statement can you write relating the three triangles in the diagram?

Problem: Identifying Similar Triangles

What similarity statement can you write relating the three triangles in the diagram?

Geometric Mean 

Problem: Finding the Geometric Mean

What is the geometric mean of 6 and 15?

Problem: Finding the Geometric Mean

What is the geometric mean of 4 and 18?

Problem: Finding the Geometric Mean

What is the geometric mean of 5 and 12?

Corollary 1 to 7-3Corollary If… Then…

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.

CD =

Corollary 2 to 7-3Corollary If… Then…

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 hypotenuse and the length of the segment of the hypotenuse adjacent

to the leg.

AC =

Problem: Using the Corollaries

What are the values of x and y?

Problem: Using the Corollaries

What are the values of x and y?

Problem: Using the Corollaries

What are the values of x and y?

Problem: Finding a Distance

You are preparing for a robotics competition using the setup shown here. Points A, B, and C are located so that AB = 20 in., and AB is perpendicular to BC. Point D is located on AC so that BD is perpendicular to AC and DC = 9in. You program the robot to move from A to D and to pick up the plastic bottle at D. How far does the robot travel from A to D?

Problem: Finding a Distance

From point D, the robot must turn right and move to point B to put the bottle in the recycling bin. How far does the robot travel from D to B?

Problem: Finding a Distance

Maggie has a kite with the dimensions shown below. What is the width of the kite?

After: Lesson Check Find the geometric mean of each pair of numbers.1. 4 and 92. 4 and 12

3. Identify the following in triangle RST. a. The hypotenuseb. The segments of the hypotenusec. The segments of the hypotenuse adjacent to leg ST

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