# Triangles in a Trapezoid - Geometric Mean

- Author:
- James R Olsen

ABCD is a trapezoid.
Segments AC and BD are diagonals meeting at E.
Prove: The areas of each triangle on a leg of the trapezoid is the geometric mean of the areas of the triangles on the bases of the trapezoid.
[Note: The Geometric Mean of two numbers and is .]
Restated: Prove that

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