Question

determine if triangle ijk and triangle lmn are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)
answer attempt 1 out of 2
the triangles ~ similar.

Explanation:

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

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle IJK\), if two angles are \(41^{\circ}\) and \(98^{\circ}\), then the third angle \(\angle I=180^{\circ}-(41^{\circ} + 98^{\circ})=41^{\circ}\)

Step2: Compare angles of the two triangles

In \(\triangle IJK\), angles are \(41^{\circ},98^{\circ},41^{\circ}\). In \(\triangle LMN\), angles are \(41^{\circ},98^{\circ}\) (since two angles are given as \(41^{\circ}\) and \(98^{\circ}\), and sum of angles in a triangle is \(180^{\circ}\), the third angle will be \(41^{\circ}\)). 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)

Answer:

The triangles are similar.