Question

are these triangles similar? yes no

Explanation:

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

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle TRS\), if two angles are \(49^{\circ}\) and \(97^{\circ}\), then the third angle \(R\) is \(180-(49 + 97)=34^{\circ}\)

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

For \(\triangle FGH\), if two angles are \(97^{\circ}\) and \(53^{\circ}\), then the third angle \(H\) is \(180-(97 + 53)=30^{\circ}\)

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

Since the angles of \(\triangle TRS\) (\(49^{\circ},97^{\circ},34^{\circ}\)) and \(\triangle FGH\) (\(97^{\circ},53^{\circ},30^{\circ}\)) are not equal in pairs, the triangles do not satisfy the AA (Angle - Angle) similarity criterion.

Answer:

no