Question

determine if triangle qrs and triangle tuv are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.) answer attemp are are not the triangles similar.

Explanation:

Step1: Calculate the ratio of corresponding sides

For triangle \(QRS\) and \(TUV\), we consider the sides adjacent to the \(52^{\circ}\) angle.
The ratio of the sides is \(\frac{19}{57}=\frac{1}{3}\) and \(\frac{18}{54}=\frac{1}{3}\)

Step2: Check the angle - side - angle (ASA) similarity criterion

Since the included angles (\(52^{\circ}\)) are equal and the ratios of the adjacent sides are equal (\(\frac{1}{3}\)), by the SAS (Side - Angle - Side) similarity criterion, the two triangles are similar.

Answer:

The triangles are similar.