Question

determine if triangle klm and triangle nop 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 two - pairs of corresponding angles are equal. In \(\triangle KLM\), we have two angle measures given as \(68^{\circ}\) and \(67^{\circ}\). In \(\triangle NOP\), we have two angle measures given as \(68^{\circ}\) and \(45^{\circ}\).

Step2: Calculate the third - angle of \(\triangle KLM\)

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the third angle of \(\triangle KLM\) be \(x\). Then \(x = 180-(68 + 67)=45^{\circ}\).

Step3: Compare angles

In \(\triangle KLM\), the angles are \(68^{\circ}\), \(67^{\circ}\), and \(45^{\circ}\). In \(\triangle NOP\), the angles are \(68^{\circ}\), \(45^{\circ}\), and \(180-(68 + 45)=67^{\circ}\). Since the three pairs of corresponding angles of \(\triangle KLM\) and \(\triangle NOP\) are equal, the two triangles are similar.

Answer:

The triangles are similar because the three pairs of corresponding angles are equal.