Question

if E and F are the points on diagnol AC of a parallelogram ABCD such that AE=CF,then show that BFDE is a parallelogram

Answer 1

GIVEN - ABCD IS A PARALLELOGRAM
AE=CF
TO PROVE THAT - BFDE IS A PARALLELOGRAM

PROOF - IN Δ AED N Δ BFC
AD=BC (OPP. SIDE OF PARALLELOGRAM)
ANG. DAE = ANG. BCF (ALTERNATE INTERIOR ANGLE)
AE= CF (GIVEN)
BY SAS CONG.
ΔAED IS CONG. TO Δ BFC
DE= BF (CPCT)
SLY, IN ΔDFC N Δ BEA
DF= BF (CPCT)

SINCE OPP. SIDES R EQUAL
N IN A PARALLELOGRAM, OPP. SIDES R EQUAL...

SO, BDEF IS A PARALLELOGRAM.....



HOPE IT WORKS..... THNK U