Question

are these triangles similar? yes no

Explanation:

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

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle TSR\), if two angles are \(92^{\circ}\) and \(50^{\circ}\), then the third angle \(\angle T=180^{\circ}-(92^{\circ} + 50^{\circ})=180^{\circ}-142^{\circ}=38^{\circ}\).

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

For \(\triangle GHI\), if two angles are \(92^{\circ}\) and \(52^{\circ}\), then the third angle \(\angle I=180^{\circ}-(92^{\circ}+52^{\circ})=180^{\circ}-144^{\circ} = 34^{\circ}\).

Step3: Check the similarity condition

Two triangles are similar if their corresponding angles are equal. The angles of \(\triangle TSR\) are \(38^{\circ},50^{\circ},92^{\circ}\) and the angles of \(\triangle GHI\) are \(34^{\circ},52^{\circ},92^{\circ}\). Since not all corresponding angles are equal.

Answer:

no