Question

30) Points E and Flie on diagonals AC of a parallelogram ABCD such that AE=CF. Prove that BEDF is also a parallelogram.​

Answer 1

Answer:

ABCD is a parallelogram and AE=CF

Join BD, meet AC at point O.

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.

Step-by-step explanation: