Question

In fig 2.67, PQ = 5, XY = 7.5, QR = 4, YZ = 6, PR = 6, XZ = 9, Are $∆$PQR and $∆$XYZ similar? If yes, state th test and the correspondence of similarity.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \frac{\mathrm{PQ}}{\mathrm{XY}}=\frac{5}{7.5}=\frac{2}{3} \\ \frac{\mathrm{QR}}{\mathrm{YZ}}=\frac{4}{6}=\frac{2}{3} \\ \frac{\mathrm{PR}}{\mathrm{XZ}}=\frac{6}{9}=\frac{2}{3} \\ \mathrm{Since},\mathrm{all}\mathrm{the}\mathrm{three}\mathrm{ratios}\mathrm{are}\mathrm{equal},\mathrm{we}\mathrm{have}, \\ △\mathrm{PQR}~△\mathrm{XYZ}(\mathrm{SSS}\mathrm{test}) \end{gathered}$$