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Question
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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Solution
Given: ABCD is a parallelogram and AE = CF
To show: OE = OF
Construction: Join BD, meet AC at point O.
Proof: Since, diagonals of a parallelogram bisect each other.
∴ OA = OC
And OD = OB
Now, OA = OC
And AE = CF ...[Given]
⇒ OA – AE = OC – CF
⇒ OE = OF
Thus, BFDE is a quadrilateral whose diagonals bisect each other.
Hence, BFDE is a parallelogram.
Hence proved.
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