Question

write a similarity statement.
△ ~ △

Explanation:

Step1: Check the ratios of sides

Calculate the ratios of the corresponding sides. For the sides \(48\) and \(71\), \(72\) and \(37\), \(\frac{48}{71}
eq\frac{72}{37}\). So SSS (Side - Side - Side) similarity (where \(\frac{a}{a'}=\frac{b}{b'}=\frac{c}{c'}\)) and SAS (Side - Angle - Side) similarity (where \(\frac{a}{a'}=\frac{b}{b'}\) and the included angles are equal) do not apply.

Step2: Analyze the given information

We are only given one pair of equal angles (\(\angle S=\angle P = 97^{\circ}\)). But for AA (Angle - Angle) similarity, we need two pairs of equal angles. Since we don't have enough information (only one angle is given for each triangle) to prove similarity using AA (as we can't confirm a second pair of equal angles), the triangles cannot be proven similar.

Answer:

none of the above; the triangles cannot be proven similar