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Question
E and F are points on diagonal AC of parallelogram ABCD such that AE = CF. We can conclude that, BFDE is a
E and F are points on diagonal AC of parallelogram ABCD such that AE = CF. We can conclude that, BFDE is a
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Solution
The correct option is C parallelogram
Given, ABCD is a parallelogram and AE = CF
To show that, OE = OF
Construction, Join BD, which meets 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]
Given, ABCD is a parallelogram and AE = CF
To show that, OE = OF
Construction, Join BD, which meets 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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