Question

are these triangles similar? yes no

Explanation:

Step1: Calculate the third angle of triangle \(GHI\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle GHI\), if two angles are \(57^{\circ}\) and \(31^{\circ}\), then the third angle \(\angle G=180^{\circ}-(57^{\circ} + 31^{\circ})=180^{\circ}-88^{\circ}=92^{\circ}\).

Step2: Calculate the third angle of triangle \(STR\)

For \(\triangle STR\), if two angles are \(57^{\circ}\) and \(31^{\circ}\), then the third angle \(\angle R=180^{\circ}-(57^{\circ}+31^{\circ}) = 92^{\circ}\).

Step3: Check the AA (Angle - Angle) similarity criterion

In \(\triangle GHI\) and \(\triangle STR\), \(\angle H = \angle S=57^{\circ}\), \(\angle I=\angle T = 31^{\circ}\), \(\angle G=\angle R=92^{\circ}\). By the AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), the two triangles are similar.

Answer:

yes