Question

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

Explanation:

Step1: Calculate angles in \(\triangle IJK\)

In \(\triangle IJK\), using the angle - sum property of a triangle (\(\angle I+\angle J+\angle K = 180^{\circ}\)). Given \(\angle J=71^{\circ}\) and \(\angle I = 62^{\circ}\), then \(\angle K=180^{\circ}-(71^{\circ}+62^{\circ})=180^{\circ}-133^{\circ}=47^{\circ}\).

Step2: Check for similarity

In \(\triangle FGH\), \(\angle G = 71^{\circ}\) and \(\angle H=47^{\circ}\). In \(\triangle IJK\), \(\angle J = 71^{\circ}\) and \(\angle K=47^{\circ}\). 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), since \(\angle J=\angle G = 71^{\circ}\) and \(\angle K=\angle H = 47^{\circ}\), \(\triangle FGH\sim\triangle IJK\).

Answer:

\(\triangle FGH\) is similar to \(\triangle IJK\)