In Fig. 8.11, AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF.

Question

Philoid · Accepted Answer

In quad ABED, we have AB||DE and AB = DE

ABED is a parallelogram.

AD||BE and AD = BE

Now, in quad ACFD, we have

AC||FD and AC = FD

ACFD is a parallelogram.

AD||CF and AD = CF

AD = BE = CF and CF||BE

Now, in quad BCFE,

BE = CF and BE||CF.

BCFE is a parallelogram.

BC = EF and BC||EF

Hence, proved.