• # question_answer X and Y are points on the sides AB and AC respectively of a triangle ABC such that $\frac{AX}{AB},AY=2\,cm$ and $YC=6\,cm$. Find whether $XY\parallel BC$ or not.

 $\frac{AX}{AB}=\frac{1}{4}$ i.e.,                               $AX=1K,\text{ }AB=4K$    (K- constant) $\therefore BX=AB-AX$ $=4K-1K=3K$ Now,                 $\frac{AX}{XB}=\frac{1K}{3K}=\frac{1}{3}$ And,                 $\frac{AY}{YC}=\frac{2}{6}=\frac{1}{3}$ $\frac{AX}{XB}=\frac{AY}{YC}$ $\therefore XY\parallel BC$         (By converse of Thales? theorem)