Question

which triangle is similar to △pqr? (triangles are not drawn to scale)

Explanation:

Step1: Recall similarity - ratio rule

For two triangles to be similar, the ratios of their corresponding sides must be equal.

Step2: Calculate side - length ratios for \(\triangle PQR\)

In \(\triangle PQR\), the side - lengths are \(PQ = 26\), \(QR=30\), \(PR = 22\).

Step3: Check option A

For option A, the side - lengths are \(13\), \(15\), \(11\). The ratios of the sides of \(\triangle PQR\) to the sides of the triangle in option A are: \(\frac{26}{13}=2\), \(\frac{30}{15} = 2\), \(\frac{22}{11}=2\). The ratios of the corresponding sides are equal.

Step4: Check option B

For option B, the side - lengths are \(15\), \(13\). Since \(\triangle PQR\) has three sides and this option has only two side - length values shown, we can't establish similarity.

Step5: Check option C

For option C, the side - lengths are \(8\), \(15\). The ratios of the sides of \(\triangle PQR\) to the sides of the triangle in option C: \(\frac{26}{8}=\frac{13}{4}\), \(\frac{30}{15}=2\), \(\frac{22}{?}\) (incomplete comparison as not all sides are given in proportion). Since the ratios are not equal, it is not similar.

Answer:

A. The triangle with side - lengths 13, 15, 11.