Transformation of a triangle

Problem

ABCD is a parallelogram. The line segment EF is parallel to BD. Prove the area of the triangle ABE is equal to the area of the triangle ADF.

Applet

Drag three vertices of the triangle (red points).
The area is unchanged during the motion.
Transform the triangle ABE to the triangle ADF.

The program is developed by IES Inc., Japan, the web site is http://www.ies.co.jp/math/java/iesjava.html-ssi

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