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Based on the diagram above and by definition of the geometric mean, the following relation holds true.
CD2=AD⋅BD or ADCD=CDBD
The Geometric Mean Altitude Theorem is also known as the Right Triangle Altitude Theorem and the Geometric Mean Theorem.
ADCD=CDBD
Applying the Properties of Equality, this proportion can be rewritten without fractions.
CD2=AD⋅BD