Question

1. which of the follow triangles is similar to \\( \triangle p q r \\)?

Explanation:

Step1: Calculate the ratio of sides for \(\triangle PQR\)

We have \(PQ = 21\) and \(PR=18\). Let's check the ratios for each option.
For option D:
The sides are \(17.5\) and \(15\).

Step2: Calculate the ratio of corresponding sides

The ratio of \(PQ\) to the side in option D: \(\frac{21}{17.5}=\frac{21\times2}{17.5\times2}=\frac{42}{35} = 1.2\)
The ratio of \(PR\) to the side in option D: \(\frac{18}{15}=\frac{18\div3}{15\div3}=\frac{6}{5}=1.2\)
Since the ratios of the corresponding sides are equal and the included angles (the angles between the sides) are equal (by the SAS - Side - Angle - Side similarity criterion, as the angles are marked as equal in the non - labeled part of the triangles), \(\triangle PQR\) and the triangle in option D are similar.

Answer:

D.