(Q18) In the given figure, LM ∥ CM and LN ∥ CD. Prove that
AM
AB
 =
AN
AD
 .
ABCDMNL

Answer :

Given :LM ∥ CB and LN ∥ CD In ∆ABC, LM ∥ BC (given) Hence,

AM
 =
LC
   ⇒
MB
AM
 =
LC
AL

Adding '1' on both sides.

 + 1 =
+ 1
MB +
AM
 =
+ AL
AL
AM
 =
AC
 ⇒
AM
AB
 =
AL
AC
 .....(1)

Similarly in ∆ACD, LN ∥ CD

∴
AN
ND
 =
AL
LC
AN
 =
LC
 ⇒
ND
AN
 + 1 =
LC
AL
 + 1

Adding '1' on both sides.

+ AN
AN
 =
+ AL
AL
AN
 =
AC
 ⇒
AN
AD
 =
AL
AC
 .....(2)

From (1) and (2)

∴
AM
AB
 =
AN
AD