In the figure (1) given below, ABCD and ABEF are parallelograms. Prove that

(i) CDFE is a parallelogram.

(ii) FD = EC

(iii) △AFD ≅ △BEC.

(i) DC || AB and DC = AB [∵ ABCD is a || gm] ………. (1)

FE || AB and FE = AB [∵ ABEF is a || gm] ………..(2)

∴ DC || FE and DC = FE [From (1) and (2)]

Hence, proved that CDFE is a || gm.

(ii) Since, CDEF is a || gm.

So, FD = EC (As opposite sides of a || gm are equal)

Hence, proved that FD = EC.

(iii) In ∆AFD and ∆BEC, we have

AD = BC [Opposite sides of || gm ABCD are equal]

AF = BE [Opposite sides of || gm ABEF are equal]

FD = CE [Opposite sides of || gm CDFE are equal]

Hence, ∆AFD ≅ ∆BEC by S.S.S axiom of congruency

Hence, proved that ∆AFD ≅ ∆BEC.