Question

△abc and △def are shown below.
which statement is true?
△abc is similar to △def.
△abc is not similar to △def.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Calculate the measure of angle \( B \) in \( \triangle ABC \)

The sum of angles in a triangle is \( 180^{\circ} \). So, \( \angle B=180^{\circ}-(15^{\circ} + 45^{\circ})=120^{\circ} \)

Step2: Compare angles of \( \triangle ABC \) and \( \triangle DEF \)

In \( \triangle ABC \), angles are \( 15^{\circ},45^{\circ},120^{\circ} \). In \( \triangle DEF \), angles are \( 15^{\circ}( \text{since }180^{\circ}-120^{\circ}-45^{\circ}=15^{\circ}),45^{\circ},120^{\circ} \).
By AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), \( \triangle ABC\sim\triangle DEF \)

Answer:

\( \triangle ABC \) is similar to \( \triangle DEF \)