Question

In the Fig. 3.32. ABCD is a parallelogram. Points E and F lie on diagonal AC such that AE = CF. Is
quadrilateral BFDE a parallelogram?
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Answer 1

Answer:

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Answer 2

Proof Since,

Diagonals of a parallelogram bisect each other. Thus, BFDE is a quadrilateral whose diagonals bisect each other.

Hence, BFDE is a parallelogram.

Hence proved.

Hi ,

Draw a rough diagram ,

Join BD , meeting AC to O,

Since the diagonals of a

parallelogram bisect each other ,

We have

OD = OB

and

OA = OC

Also , AE = FC ( given )

Now ,

OA - AE = OC - FC

OE = OF

In quadrilateral DFBE ,

OD = OB

and OE = OF.

As the diagonals of the quadrilateral

DFBE bisect each other.

Therefore ,

Quadrilateral DFBE is a parallelogram .

I hope this helps you.

:)