Question

in the figure if LM//CB and LN // CD prove that AM/AN=AB/AD​

Answer 1

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GIVEN :-

LM || CB

LN || CD

TO PROVE :-

AM/AN = AB/AD

PROOF :-

In △ABC,

LM∥BC

∴ By proportionality theorem,

AM/AB=AL/AC............(1)

Similarly,

In △ADC,

LN∥CD

∴ By proportionality theorem,

AN/AD=AL/AC............(2)

∴ from (1) and (2),

AM/AB=AN/AD

Answer 2

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In the given figure, we can see, LM || CB,

By using basic proportionality theorem, we get,

AM/AB = AL/AC……………………..(i)

Similarly, given, LN || CD and using basic proportionality theorem,

∴AN/AD = AL/AC………………(ii)

From equation (i) and (ii), we get,

AM/AB = AN/AD

Hence, proved.