Question

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

Answer 1

$$\begin{gathered} \mathrm{In}△\mathrm{ABC}\text{and}△\mathrm{PQR}, \\ \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{4.6}{2.3}=2....\left(1\right) \\ \frac{\mathrm{BC}}{\mathrm{QR}}=\frac{10}{5}=2....\left(2\right) \\ \frac{\mathrm{AC}}{\mathrm{PR}}=\frac{8}{4}=2....\left(3\right) \\ \mathrm{From}\mathrm{equations}\left(1\right),\left(2\right)\mathrm{and}\left(3\right),\mathrm{we}\mathrm{get}: \\ \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{BC}}{\mathrm{QR}}=\frac{\mathrm{AC}}{\mathrm{PR}}=2 \\ \mathrm{Therefore},\mathrm{by}\text{the}\mathrm{SSS}\mathrm{similarity}\mathrm{test}, \\ △\mathrm{ABC}~△\mathrm{PQR}. \end{gathered}$$