Question

In fig. 2.47, as per the information given, are the $△$PRQ and $△$AED similar? Justify your answer.

Answer 1

$$\begin{gathered} \mathrm{As}\frac{4}{8}=\frac{6}{12}=\frac{5}{10} \\ \Rightarrow \frac{\mathrm{PQ}}{\mathrm{AD}}=\frac{\mathrm{QR}}{\mathrm{DE}}=\frac{\mathrm{PR}}{\mathrm{AE}} \\ \mathrm{Now},\mathrm{in}△\mathrm{PQR}\mathrm{and}△\mathrm{ADE},\mathrm{we}\mathrm{have}: \\ \frac{\mathrm{PQ}}{\mathrm{AD}}=\frac{\mathrm{QR}}{\mathrm{DE}}=\frac{\mathrm{PR}}{\mathrm{AE}} \\ \therefore △\mathrm{PQR}\cong △\mathrm{ADE}(\mathrm{SSS}\mathrm{similarity}\mathrm{test}) \end{gathered}$$