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E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

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Best answer

Construction:

Join BD, meeting AC at O.

According to the question,

Since diagonals of a parallelogram bisect each other,

We get,

OA = OC and OD = OB.

And,

OA = OC and AE = CF,

OA – AE = OC – CF

OE = OF

So, BFDE is a quadrilateral whose diagonals bisect each other.

Hence, BFDE is a parallelogram.

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