Question

DF is parallel tBC and AD/DC =CE/BE prove that FDEC is a parallelogram​

Answer 1

Step-by-step explanation:

There is a mistake in this question. If DC is parallel to BC then AD/BC is not correct. It should be AD/DC. I am attaching a rough sketch with this question, by which you can understand clearly.

Solution:-

We have DF || BC

⇒ AD/DC = AF/FB .....(1)

Given :-

AD/DC = CE/BE ........(2)

From (1) and (2), we have

AF/FB = CE/EB

⇒ BE/EC = BF/AF

⇒ EF || CA

Now, DF || BC and EF || CA

⇒ DF || CE and EF || CD

Hence FDCE is a parallelogram.

Proved.