Question

determine if triangle fgh and triangle ijk are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)

Explanation:

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

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle FGH\), if two angles are \(49^{\circ}\) and \(82^{\circ}\), then the third angle \(\angle F=180-(49 + 82)=49^{\circ}\).

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

For \(\triangle IJK\), if two angles are \(82^{\circ}\) and \(50^{\circ}\), then the third angle \(\angle I=180-(82 + 50)=48^{\circ}\).

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

The AA similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. In \(\triangle FGH\), the angles are \(49^{\circ},82^{\circ},49^{\circ}\). In \(\triangle IJK\), the angles are \(82^{\circ},50^{\circ},48^{\circ}\). There are no two - angle pairs that are equal.

Answer:

The triangles are not similar.