Forming Ratios
In some cases the same length may be used in two ratios, because it is common to the two similar triangles being considered.
For example, in  side  is common to both triangles, so if we use the ratios  for both, we have:  . If we cross-multiply, this gives  . In other words,  . We call h the geometric mean of d and e. That is, the altitude to the hypotenuse of a right triangle is the geometric mean of the segments into which the hypotenuse is split. |
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There are actually three geometric means that come from the above diagram:
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Similar Triangles |
Proportion |
Geometric Mean |
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Date last modified: August 6, 2008.
