In parallelogram ABCD, the perpendiculars BE and DF are drawn to the diagonal AC.

In parallelogram ABCD, the perpendiculars BE and DF are drawn to the diagonal AC. Prove that segments BF and DE are equal.

Since ABCD is a parallelogram, then AB = CD, BC = AD, angle ABC = ADC, then triangles ABC and ADC are equal on two sides and the angle between them.
B and D are the corresponding vertices of equal triangles ABC and ADC, and the segments BE and DF are the heights drawn from the corresponding vertices, then BE = DF, which was required to prove.



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