Prove that a line drawn parallel to one side of a triangle to intersect the other two sides in distinct points divides the other two sides in the…

In \(\displaystyle \Delta \mathrm{ABC}, \mathrm{LM} \| \mathrm{CB}\) \[\frac{\mathrm{AM}}{\mathrm{MB}}=\frac{\mathrm{AL}}{\mathrm{LC}} \quad \text {--- (1) } \] In \(\displaystyle \Delta \mathrm{ADC}, \mathrm{LN} \| \mathrm{CD}\) \[\frac{\mathrm{AN}}{\mathrm{ND}}=\frac{\mathrm{AL}}{\mathrm{LC}} \quad \text {--- (2) } \] from ($\displaystyle 1$) and ($\displaystyle 2$), we have \[\frac{\mathrm{AM}}{\mathrm{MB}}=\frac{\mathrm{AN}}{\mathrm{ND}} \]