Question

are these triangles similar? yes no

Explanation:

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

The sum of angles in a triangle is \( 180^{\circ} \). Let the third - angle of \( \triangle FEO \) be \( \angle O \). Then \( \angle O=180^{\circ}-(30^{\circ} + 96^{\circ})=180^{\circ}-126^{\circ}=54^{\circ}\).

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

Let the third - angle of \( \triangle VTU \) be \( \angle U \). Then \( \angle U=180^{\circ}-(30^{\circ}+96^{\circ}) = 54^{\circ}\).

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

In \( \triangle FEO \) and \( \triangle VTU \), \( \angle F=\angle V = 30^{\circ}\), \( \angle E=\angle T=96^{\circ}\), and \( \angle O=\angle U = 54^{\circ}\). By the AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar), the two triangles are similar.

Answer:

yes