Question

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

Answer 1

$$\begin{gathered} \mathrm{In}△\mathrm{ABC}\&△\mathrm{PQR}, \\ \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{24}{12}=2...\left(1\right) \\ \frac{\mathrm{BC}}{\mathrm{QR}}=\frac{7}{5}...\left(2\right) \\ \frac{\mathrm{AC}}{\mathrm{PR}}=\frac{25}{13}...\left(3\right) \\ \mathrm{From}\mathrm{equations}\left(1\right),\left(2\right)\mathrm{and}\left(3\right),\mathrm{we}\mathrm{get}: \\ \frac{\mathrm{AB}}{\mathrm{PQ}}\ne \frac{\mathrm{BC}}{\mathrm{QR}}\ne \frac{\mathrm{AC}}{\mathrm{PR}} \\ \mathrm{Thus},△\mathrm{ABC}\mathrm{and}△\mathrm{PQR}\mathrm{are}\mathrm{not}\mathrm{similar}. \end{gathered}$$