# Right-Triangle Elements, Metric Relations and Pythagorean Theorem

## Mean Proportional or Geometric mean

Mean Proportional (or geometric mean) of the given segments m and n is the segment h which, with the given segments, form the following proportion:

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Therefore,

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or

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Thus, the following linguistic representation can be used to describe the metric relationship

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The height to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.

Use a linguistic representation to represent the following metric relationship in the right triangle

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Use a linguistic representation to represent the following metric relationship in the right triangle

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## Pythagorean theorem

Use a linguistic representation to represent the Pythagorean theorem

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