Question

In the fig 2.46 seg SK $\parallel$ seg MP $\parallel$ seg TN. Are $△$SAK, $△$MAP and $△$TAN similar? If yes, state the test of similarity.

Answer 1

$$\begin{gathered} \mathrm{As}\mathrm{SK}\parallel \mathrm{MP}\parallel \mathrm{TN},\mathrm{we}\mathrm{have}: \\ \angle \mathrm{ASK}=\angle \mathrm{AMP}=\angle \mathrm{ATN}(\mathrm{Alternate}\mathrm{angles})...\left(\mathrm{i}\right) \\ \mathrm{In}△\mathrm{SAK},△\mathrm{MAP}\mathrm{and}△\mathrm{TAN},\mathrm{we}\mathrm{have}: \\ \angle \mathrm{SAK}=\angle \mathrm{MAP}=\angle \mathrm{TAN}=25° \\ \angle \mathrm{ASK}=\angle \mathrm{AMP}=\angle \mathrm{ATN}\left[\mathrm{From}\right(\mathrm{i}\left)\right] \\ \therefore △\mathrm{SAK},△\mathrm{MAP}\mathrm{and}△\mathrm{TAN}\mathrm{are}\mathrm{all}\mathrm{similar}\mathrm{by}\hspace{0.17em}\mathrm{AA}\hspace{0.17em}\mathrm{similarty}\mathrm{test}. \end{gathered}$$