In figure DF is parallel to BC and AD/BC=CE/BE.prove that FDCE is parallelogram
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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.
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.
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