Question

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

Answer 1

Given: PQ = 5, XY = 7.5, QR = 4,YZ = 6. PR = 6, XZ = 9
Now, $\frac{PQ}{XY}=\frac{5}{7.5}=\frac{2}{3}$
$\frac{QR}{YZ}=\frac{4}{6}=\frac{2}{3}$
$\frac{PR}{XZ}=\frac{6}{9}=\frac{2}{3}$
Since, $\frac{PQ}{XY}=\frac{QR}{YZ}=\frac{PR}{XZ}$
Hence, $△PQR\sim △XYZ$ (SSS rule)