Question

In the figure LM || CB and LN || CD.
Prove that AM/AB = AN/AD

Answer 1

ANSWER

In △ABC,

LM∥BC

∴ By proportionality theorem,

AB

AM

=

AC

AL

............(1)

Similarly,

In △ADC,

LN∥CD

∴ By proportionality theorem,

AD

AN

=

AC

AL

............(2)

∴ from (1) and (2),

AB

AM

=

AD

AN

Answer 2

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

By using basic proportionality theorem, we get,

AM/MB = AL/LC …..(i)

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

∴ AN/AD = AL/LC ……(ii)

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

AM/MB = AN/AD

Hence, proved.