△pqr and △stu are shown below.\nwhich statement is true?\n△pqr is similar to △stu.\n△pqr is not similar to…

Explanation:

Step1: Recall Similarity Criteria

To determine if two triangles are similar, we can use criteria like AA (Angle - Angle), SAS (Side - Angle - Side) similarity, SSS (Side - Side - Side) similarity. For SAS similarity, two sides of one triangle must be proportional to two sides of the other triangle, and the included angle must be equal.

Step2: Analyze the Given Triangles

• In (\triangle PQR), we see that (PR = PQ) (marked with equal tick marks), so (\triangle PQR) is isosceles with (\angle P) as the vertex angle.

• In (\triangle STU), we only know that (\angle S) is equal to (\angle P) (marked with the same arc). But we don't know if the sides around (\angle P) and (\angle S) are proportional. We know (PR = PQ) in (\triangle PQR), but we have no information about the lengths of (ST) and (SU) relative to each other or relative to (PQ) and (PR).

• For SAS similarity, we need (\frac{PQ}{ST}=\frac{PR}{SU}) and (\angle P=\angle S). We know (\angle P = \angle S), but we don't know if (\frac{PQ}{ST}=\frac{PR}{SU}) because we don't know the lengths of (ST), (SU) compared to (PQ), (PR). We only know (PQ = PR), but we don't know if (ST = SU) or the ratio between the sides. So we can't confirm SAS similarity. We also don't have enough information for AA (we only know one angle is equal) or SSS (we don't know side lengths).

Answer:

There is not enough information to determine whether the triangles are similar.