Question

directions: determine whether each pair of triangles is similar. if they are, justify your reasoning.

yes they are similar by aa similarity
yes they are similar by sas similarity
no, they are not similar
yes they are similar by sss similarity

Explanation:

Step1: Calculate the ratios of corresponding sides

For \(\triangle OTY\) and \(\triangle EFC\),
The ratio of the sides \(TY\) and \(FC\) is \(\frac{TY}{FC}=\frac{2}{3}\)
The ratio of the sides \(OT\) and \(EF\) is \(\frac{OT}{EF}=\frac{3}{4.5}=\frac{3}{\frac{9}{2}}=\frac{2}{3}\)
The ratio of the sides \(OY\) and \(EC\) is \(\frac{OY}{EC}=\frac{3}{4.5}=\frac{2}{3}\)

Step2: Check the similarity criterion

Since \(\frac{TY}{FC}=\frac{OT}{EF}=\frac{OY}{EC}=\frac{2}{3}\), by the SSS (Side - Side - Side) similarity criterion, the two triangles are similar.

Answer:

yes they are similar by SSS similarity