Question

E&F are points on diagonals ac of parallelogram ABCD such that AE=CF. Show that BFDE is a parallelogram.

Answer 1

Hello,

Given: E and F are points on diagonal AC of parallelogram ABCD with AE=CF

To prove: BFDE is a parallelogram

Construction: Join DE, DF, BE, BF, DB

Proof:

∵ diagonals of a ║gm bisect each other

⇒ OA = OC

   OD = OB

∵ OA = OC and AE = CF (Given)

  OA-AE = OC-CF

  OE = OF

∵ BFDE is a quadrilateral whose diagonals bisect each other

⇒ BFDE is a ║gm, hence proved

HOPE THIS HELPS ^_^