Geometric means and similarity in right triangles
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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.

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Geometric Means and Similarity in Right Triangles

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Geometric means and similarity in right triangles

Geometric Means and Similarity in Right Triangles


Warm ups

Warm-ups


Geometric means

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

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

Example

  • Identify the similar triangles and write a similarity statement.


Using similarity to solve for segment lengths

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.


Example1

Example

  • Solve for x, y and z.


Example2

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?


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