Question

In the following figure, if LM || CB and LN || CD, prove that \(\frac{AM}{AB}=\frac{AN}{AD}\)

Answer 1

To Prove: \(\frac{AM}{AB}=\frac{AN}{AD}\)

In the given figure, LM || CB
By using the basic proportionality theorem, we obtain

\(\frac{AM}{AB}=\frac{AL}{AC}\) ......(i)

Similarly, LN || CD
∴\(\frac{AN}{AD}=\frac{AL}{AC}\) ......(ii)

From (i) and (ii) we obtain 
\(\frac{AM}{AB}=\frac{AN}{AD}\)

Hence Proved