Geometric Mean in Right Triangles
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Learning Objective
I can apply the geometric mean to find missing side lengths in right triangles.
Lesson Flow
Watch Video
The Geometric Mean Theorem | Geometry | Math Video Central
Math Video Central
Guided Notes
Key concepts students will learn:
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The Geometric Mean Theorem states that in a right triangle, the altitude drawn to the hypotenuse divides the hypotenuse into two segments.
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The altitude is the geometric mean of the two segments, and each leg of the triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.
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If BD = 9 and AD = 16, then the altitude h (CD) is the square root of 9 times 16, which equals 12.
Practice
9 questions • Multiple choice & Short answer & Fill in the blank
Exit Ticket
“In right triangle XYZ, altitude YW is drawn to hypotenuse XZ. If XW = 4 and ZW = 25, find the length of altitude YW. Show your work.”
Teacher Guide
Get the complete package:
- Answer keys for all questions
- Differentiation strategies
- Extension activities
- Printable student handouts
