AD and PS are angle bisectors of ∠ A and ∠ P of triangles ABC and PQR. If ABC ∼ PQR, prove that ACD ∼ PRS.

\[\Delta \mathrm{ABC} \sim \Delta \mathrm{PQR} \] \(\displaystyle \therefore \angle \mathrm{BAC}=\angle \mathrm{QPR}\) \[\Rightarrow \frac{1}{2} \angle \mathrm{BAC}=\frac{1}{2} \angle \mathrm{QPR} \] \(\displaystyle \Rightarrow \angle 2=\angle 4\) and \(\displaystyle \angle \mathrm{C}=\angle \mathrm{R} \therefore \triangle \mathrm{ACD} \sim \triangle \mathrm{PRS}\)