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Question:

In Fig., if LM||CB and LN||CD, prove that AM/AB = AN/AD.

Solution:

In ΔABC, LM||BC ∴ By proportionality theorem, AM/AB = AL/AC (1)
Similarly, In ΔADC, LN||CD ∴ By proportionality theorem, AN/AD = AL/AC (2)
∴ from (1) and (2), AM/AB = AN/AD