Question

determine the relationship between the triangles.

Explanation:

Step1: Calculate the third angle of the first triangle

The sum of angles in a triangle is \(180^{\circ}\). For the first triangle, if two angles are \(78^{\circ}\) and \(32^{\circ}\), then the third angle \(\theta_1=180-(78 + 32)=70^{\circ}\)

Step2: Compare angles with the second triangle

The second triangle has angles \(70^{\circ}\) and \(78^{\circ}\). Since two pairs of angles (\(70^{\circ}\) and \(78^{\circ}\)) are equal in the two triangles. 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.

Answer:

AA~