geometric mean

Author:
Kevin Taylor
Topic:
Geometric Mean, Means
The figure shown gives a right triangle with altitude draw from point D to the base. Point D is movable.
GeoGebra Applet
Before you show the three triangles, consider the following:
  • How many triangles are there? How do the angles of the triangles compare?
Click "Show 3 triangles" button. Does this confirm your suspicion?
  • What parts correspond? What are some similarity ratios you can calculate? Are they the same when you move point D?
Click Show ratio 1 and show ratio 2. Move point D around. Does the ratio change? Why or Why not? Click show g^2. Move point D around and observe how it changes. Then click show h times d. How do they compare? Move point D around and see if it is always true.

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