Question

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

Explanation:

Step1: Calculate the ratio of corresponding sides

For triangle \(PQR\) and \(STU\), we consider the ratio of the sides. Let's assume the sides \(PR = 4\), \(PQ=6\) in \(\triangle PQR\) and \(TU = 15\), \(SU = 20\) in \(\triangle STU\).
The ratio of \(PR\) to \(TU\) is \(\frac{4}{15}\), and the ratio of \(PQ\) to \(SU\) is \(\frac{6}{20}=\frac{3}{10}\). Since \(\frac{4}{15}
eq\frac{3}{10}\), the sides are not in proportion.

Step2: Check the angle - side - angle (ASA) or side - angle - side (SAS) similarity criteria

For SAS similarity, we need two sides in proportion and the included angle equal. Here, the included angle is \(40^{\circ}\) in both triangles. But as we saw in Step 1, the sides adjacent to the \(40^{\circ}\) angle (\(PR\) and \(PQ\) in \(\triangle PQR\), \(TU\) and \(SU\) in \(\triangle STU\)) are not in proportion.

Answer:

The triangles are not similar.