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Geometric Means and Similarity in Right Triangles

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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  1. Geometric Means and Similarity in Right Triangles

  2. Warm-ups

  3. 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

  4. 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

  5. Example • Identify the similar triangles and write a similarity statement.

  6. 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.

  7. Example • Solve for x, y and z.

  8. 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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