Question

In the given figure, there are two triangles. State whether the triangles are similar and give reasons in support of your answer.

Answer 1

$$\begin{gathered} \mathrm{In}△\mathrm{APB}\mathrm{and}△\mathrm{CPD}, \\ \frac{\mathrm{AP}}{\mathrm{CP}}=\frac{3}{5}...\left(1\right) \\ \angle \mathrm{APB}=\angle \mathrm{CPD}...\left(2\right)[\mathrm{Vertically}-\mathrm{opposite}\mathrm{angles}] \\ \frac{\mathrm{PB}}{\mathrm{PD}}=\frac{3}{5}...\left(3\right) \\ \mathrm{From}\mathrm{equations}\left(1\right),\left(2\right)\mathrm{and}\left(3\right),\mathrm{we}\mathrm{get}: \\ \frac{\mathrm{AP}}{\mathrm{CP}}=\frac{\mathrm{PB}}{\mathrm{PD}}=\frac{3}{5}\mathrm{and}\angle \mathrm{APB}=\angle \mathrm{CPD}. \\ \mathrm{Therefore},\mathrm{by}\text{the}\mathrm{SAS}\mathrm{test}\mathrm{of}\mathrm{similarity}, \\ △\mathrm{APB}~△\mathrm{CPD} \end{gathered}$$