# Geometric Means and Similarity in Right Triangles - PowerPoint PPT Presentation

1 / 8

Geometric Means and Similarity in Right Triangles. Warm-ups. Geometric Means. The geometric mean of two numbers is the positive square root of their product. Example 1: Find the geometric mean of 5 and 20 Example 2: Find the geometric mean of 3 and 6. Similarity in Right Triangles.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Geometric Means and Similarity in Right Triangles

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## Geometric Means and Similarity in Right Triangles

### Geometric Means

• The geometric mean of two numbers is the positive square root of their product.

• Example 1: Find the geometric mean of 5 and 20

• Example 2: Find the geometric mean of 3 and 6

### Similarity in Right Triangles

• The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle.

A

### Example

• Identify the similar triangles and write a similarity statement.

### Using Similarity to Solve for Segment Lengths

• You can use similarity to set up a proportion and solve for a missing segment length. Remember – match the ________________________

parts of the triangles to set up the proportion.

### Example

• Solve for x, y and z.

### Example

• To estimate the height of a Douglas fir, Jan positions herself so that her lines of sight to the top of and bottom of the tree form a 90° angle. Her eyes are about 1.6 m above the ground, and she is standing 7.8 m from the tree. What is the height of the tree to the nearest meter?