Question

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

Explanation:

Step1: Recall the AA (Angle - Angle) similarity criterion

If two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.
In \(\triangle KLM\), \(\angle K=\angle M\) (base - angles of an isosceles triangle) and \(\angle L\) is the vertex angle. In \(\triangle NOP\), \(\angle N = \angle P\) (base - angles of an isosceles triangle) and \(\angle O\) is the vertex angle. Let \(\angle L=\angle O\) (given by the markings).
Since the sum of angles in a triangle is \(180^{\circ}\), if \(\angle L=\angle O\), then \(\angle K=\angle M=\frac{180^{\circ}-\angle L}{2}\) and \(\angle N=\angle P=\frac{180^{\circ}-\angle O}{2}\). So \(\angle K=\angle N\) and \(\angle M=\angle P\)

Answer:

\(\triangle KLM\) is similar to \(\triangle NOP\)