Question

which rule explains why these scalene triangles are similar?

Explanation:

Step1: Find the third angle of triangle \( \triangle EHD \)

The sum of angles in a triangle is \( 180^{\circ} \). For \( \triangle EHD \), if two angles are \( 49^{\circ} \) and \( 33^{\circ} \), then the third angle \( \angle EHD=180^{\circ}-(49^{\circ} + 33^{\circ})=98^{\circ} \). Also, \( \angle FHG=\angle EHD \) (vertical - angles are equal).

Step2: Check the AA (Angle - Angle) similarity criterion

In \( \triangle EHD \) and \( \triangle FHG \), we have two pairs of equal angles. \( \angle D=\angle F = 33^{\circ} \) (given) and \( \angle EHD=\angle FHG \) (vertical angles). 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.

Answer:

The AA (Angle - Angle) similarity criterion.