Question

In fig 2.48, $\angle$SRP = 90$°$ and seg RV $\perp$seg PS. state whether
(i) $△$SRP$~$$△$SVR
(ii) $△$SRP$~$$△$RVP
(iii) $△$SVR$~$$△$RVP

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{In}△\mathrm{SRP}\mathrm{and}△\mathrm{SVR},\mathrm{we}\mathrm{have}: \\ \angle \mathrm{PSR}=\angle \mathrm{VSR}\left(\mathrm{Common}\right) \\ \angle \mathrm{SRP}=\angle \mathrm{SVR}=90°\left(\mathrm{Given}\right) \\ \therefore △\mathrm{SRP}\cong △\mathrm{SVR}(\mathrm{AA}\hspace{0.17em}\mathrm{similarity}\mathrm{test}) \\ \left(\mathrm{ii}\right)\mathrm{In}△\mathrm{SRP}\mathrm{and}△\mathrm{RVP},\mathrm{we}\mathrm{have}: \\ \angle \mathrm{SPR}=\angle \mathrm{VPR}\left(\mathrm{Common}\right) \\ \angle \mathrm{SRP}=\angle \mathrm{RVP}=90°\left(\mathrm{Given}\right) \\ \therefore △\mathrm{SRP}\cong △\mathrm{RVP}(\mathrm{AA}\mathrm{similarity}\hspace{0.17em}\mathrm{test}) \\ \left(\mathrm{iii}\right)\mathrm{From}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right),\mathrm{we}\mathrm{get}: \\ △\mathrm{SRP}\cong △\mathrm{SVR}\mathrm{and}△\mathrm{SRP}\cong △\mathrm{RVP} \\ \therefore △\mathrm{SVR}\cong △\mathrm{RVP} \end{gathered}$$