Question

are these scalene triangles similar?

Explanation:

Step1: Check the ratio of corresponding sides

For triangle \( \triangle JHG\) and \( \triangle QPR\), \(\frac{JH}{QP}=\frac{60}{12} = 5\), \(\frac{HG}{PR}=\frac{40}{8}=5\)

Step2: Check the included angle

The included angle in \( \triangle JHG\) is \(30^{\circ}\) and the included angle in \( \triangle QPR\) is \(30^{\circ}\)

Since the ratio of two pairs of corresponding sides are equal and the included angles are equal, by the Side - Angle - Side (SAS) similarity criterion, the two triangles are similar.

Answer:

yes