Question

determine if triangle hij and triangle klm 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 ratios of corresponding sides

For triangle \(HIJ\) and \(KLM\), we have the following pairs of sides:
\(\frac{IJ}{LM}=\frac{22}{44}=\frac{1}{2}\)
\(\frac{HJ}{KM}=\frac{16}{32}=\frac{1}{2}\)
\(\frac{HI}{LK}=\frac{30}{60}=\frac{1}{2}\)

Step2: Apply the SSS (Side - Side - Side) similarity criterion

Since \(\frac{IJ}{LM}=\frac{HJ}{KM}=\frac{HI}{LK}=\frac{1}{2}\), by the SSS (Side - Side - Side) similarity criterion, the two triangles are similar.

Answer:

Triangle \(HIJ\) and triangle \(KLM\) are similar. We know this because the ratios of their corresponding sides are equal (\(\frac{IJ}{LM}=\frac{HJ}{KM}=\frac{HI}{LK}=\frac{1}{2}\)), which satisfies the SSS (Side - Side - Side) similarity criterion.