Question

Study the following figure & find out whether the triangles are similar ,
Give reason

Answer 1

$$\begin{gathered} \mathrm{MN}=\mathrm{MT}+\mathrm{TN}=2+4=6 \\ \mathrm{MK}=\mathrm{MP}+\mathrm{PK}=3+6=9 \\ \mathrm{Considering}△\mathrm{MTP}\&△\mathrm{MNK},\mathrm{we}\mathrm{get}: \\ \frac{\mathrm{MT}}{\mathrm{MN}}=\frac{2}{6}=\frac{1}{3} \\ \frac{\mathrm{MP}}{\mathrm{MK}}=\frac{3}{9}=\frac{1}{3} \\ \frac{\mathrm{TP}}{\mathrm{NK}}=\frac{2.5}{7.5}=\frac{1}{3} \\ \therefore \frac{\mathrm{MT}}{\mathrm{MN}}=\frac{\mathrm{MP}}{\mathrm{MK}}=\frac{\mathrm{TP}}{\mathrm{NK}} \\ \mathrm{By}\mathrm{the}\mathrm{SSS}\mathrm{test}\mathrm{of}\mathrm{similarity},\mathrm{we}\mathrm{have}: \\ △\mathrm{MTP}~△\mathrm{MNK} \end{gathered}$$