Question

34 multiple choice 1 point are the triangles similar? yes, by the sas rule. not similar. yes, by the aa rule. yes, by the ss rule.

Explanation:

Step1: Calculate the ratio of corresponding sides

For the two triangles, we have two pairs of corresponding sides.
The ratio of \(BC\) to \(B'C'\) is \(\frac{12}{4}=3\), and the ratio of \(CD\) to \(C'D'\) is \(\frac{9}{3}=3\).

Step2: Check the included angle

The included angle \(\angle C\) and \(\angle C'\) are equal (marked as equal in the figure).

Since the ratios of two pairs of corresponding sides are equal and the included angles are equal, by the SAS (Side - Angle - Side) similarity rule, the two triangles are similar.

Answer:

Yes, by the SAS rule.