Question

Points E & F lie on a diagonal AC of a parallelogram ABCD  such that AE=CF.What type of a quadrilateral is BFDE?

Answer 1

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.

:)

Answer 2

Here is the solution of the problem

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