Final answer:
In a similar triangle relationship, if PQR∼STU, the statement that must be true is D) P=R.
Step-by-step explanation:
In a similar triangle relationship, if PQR∼STU, there are certain statements that must be true. Let's go through each option to determine which one is correct.
A) PQ∥SU: This statement is not necessarily true. Just because two triangles are similar, it does not mean that their sides are parallel.
B) PQ=ST: This statement is not necessarily true either. In similar triangles, corresponding sides are proportional, but they are not necessarily equal. So this statement may or may not be true.
C) P=T: This statement is also not necessarily true. In similar triangles, only corresponding angles are congruent, not corresponding points.
D) P=R: This statement must be true in similar triangles. If two triangles are similar, it means that the corresponding angles and sides are proportional. Therefore, if PQR∼STU, it follows that P=R.
So, the correct statement is D) P=R.