Question

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.)

Explanation:

Step1: Recall similarity criterion

Two triangles are similar if their corresponding angles are equal.

Step2: Identify corresponding angles

In \(\triangle IJK\) and \(\triangle LMN\), \(\angle I = 68^{\circ}\), \(\angle J=48^{\circ}\) in \(\triangle IJK\) and \(\angle L = 68^{\circ}\), \(\angle M = 48^{\circ}\) in \(\triangle LMN\).

Step3: Apply similarity rule

Since two - pairs of corresponding angles are equal (\(\angle I=\angle L\) and \(\angle J=\angle M\)), by the AA (angle - angle) similarity criterion, \(\triangle IJK\sim\triangle LMN\).

Answer:

The triangles are similar.