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: Calculate the ratio of sides

For triangle \(IJK\) and \(LMN\), we have \(\frac{IJ}{LM}=\frac{18}{90}=\frac{1}{5}\) and \(\frac{JK}{MN}=\frac{19}{95}=\frac{1}{5}\)

Step2: Check the included angle

The included angle for \(IJ\) and \(JK\) in \(\triangle IJK\) is \(37^{\circ}\), and the included angle for \(LM\) and \(MN\) in \(\triangle LMN\) is \(37^{\circ}\)

Answer:

The triangles are similar. (By the Side - Angle - Side (SAS) similarity criterion, since the ratio of two pairs of corresponding sides is equal (\(\frac{IJ}{LM}=\frac{JK}{MN}=\frac{1}{5}\)) and the included angles are equal (\(37^{\circ}=37^{\circ}\)) )