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Question:

In Fig., DE||AC and DF||AE. Prove that BFFE=BEEC.

Solution:

In ΔABC, DE||AC ∴ By proportionality theorem, BD/DA = BE/EC (1)
Similarly, In ΔABE, DF||AE ∴ By proportionality theorem, BD/DA = BF/FE (2)
∴ from (1) and (2), BE/EC = BF/FE. Hence Proved.