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°. For \(\triangle IJK\), let the third - angle be \(\angle K\). Then \(\angle K=180^{\circ}-(63^{\circ} + 72^{\circ})=45^{\circ}\).

Step2: Compare angles of the two triangles

In \(\triangle IJK\), the angles are \(63^{\circ}\), \(72^{\circ}\), and \(45^{\circ}\). In \(\triangle LMN\), the angles are \(45^{\circ}\) and \(63^{\circ}\). The third - angle of \(\triangle LMN\) is \(180^{\circ}-(45^{\circ}+63^{\circ}) = 72^{\circ}\). Since the three angles of \(\triangle IJK\) are equal to the three angles of \(\triangle LMN\) (angle - angle - angle similarity criterion), the two triangles are similar.

Answer:

are