Question

are these triangles similar? yes no

Explanation:

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

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle EFG\), if \(\angle E = 35^{\circ}\) and \(\angle G=89^{\circ}\), then \(\angle F=180^{\circ}-(35^{\circ} + 89^{\circ})=180^{\circ}-124^{\circ}=56^{\circ}\)

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

For \(\triangle PQR\), if \(\angle P = 89^{\circ}\) and \(\angle Q = 30^{\circ}\), then \(\angle R=180^{\circ}-(89^{\circ}+30^{\circ})=180^{\circ}-119^{\circ} = 61^{\circ}\)

Step3: Check for angle - angle similarity

Two triangles are similar if their corresponding angles are equal. The angles of \(\triangle EFG\) are \(35^{\circ},89^{\circ},56^{\circ}\) and the angles of \(\triangle PQR\) are \(30^{\circ},89^{\circ},61^{\circ}\). Since the sets of angles are not equal, the triangles are not similar.

Answer:

no