Question

Study the following figure and state whether the triangles are similar.
Give reasons to validate your statement.

Answer 1

$$\begin{gathered} \mathrm{PX}=a+2a=3a \\ \text{In}△\mathrm{PRT}\text{and}△\mathrm{PXS}, \\ \frac{\mathrm{PR}}{\mathrm{PX}}=\frac{a}{3a}=\frac{1}{3} \\ \frac{\mathrm{RT}}{\mathrm{XS}}=\frac{2b}{3b}=\frac{2}{3} \\ \mathrm{Hence},\frac{\mathrm{PR}}{\mathrm{PX}}\ne \frac{\mathrm{RT}}{\mathrm{XS}} \\ \text{The c}\mathrm{orresponding}\mathrm{sides}\mathrm{are}\mathrm{not}\mathrm{in}\mathrm{proportion}. \\ \mathrm{Therefore},△\mathrm{PRT}\mathrm{is}\mathrm{not}\mathrm{similar}\mathrm{to}△\mathrm{PXS}. \end{gathered}$$