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.) sss: three sides proportionate sss: three sides congruent sas: two sides proportionate, included angle congruent sas: two sides + included angle congruent aa: two angles congruent

Explanation:

Step1: Calculate the ratio of the corresponding sides

For side \(PQ = 19\) and \(SU = 40\), side \(QR=25\) and \(UT = 50\).
The ratio of \(QR\) to \(UT\) is \(\frac{25}{50}=\frac{1}{2}\), and the ratio of \(PQ\) to \(SU\) is \(\frac{19}{38}=\frac{1}{2}\)

Step2: Check the included angle

The included angle \(\angle Q = 50^{\circ}\) and \(\angle T=50^{\circ}\), so \(\angle Q\cong\angle T\)

Answer:

Triangles \(PQR\) and \(STU\) are similar by the SAS (Side - Angle - Side) similarity criterion.