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: Check the ratio of sides

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

Step2: Check the included angle

The included angle \(\angle J = 37^{\circ}\) and \(\angle M=37^{\circ}\)

Since the ratio of two sides is equal (\(\frac{IJ}{MN}=\frac{JK}{ML}\)) and the included angles (\(\angle J\) and \(\angle M\)) are congruent, by the SAS (Side - Angle - Side) similarity criterion.

Answer:

Triangle \(IJK\) and triangle \(LMN\) are similar by the SAS similarity criterion.