Among the given statements regarding triangles PQR and STU, only statement F is true, stating that ∠Q is congruent to ∠T, based on their corresponding coordinates.
Let's evaluate the given statements using the coordinates of the vertices of triangles PQR and STU:
Coordinates:
P(-5,2), Q(-2,6), R(-1,3) for triangle PQR
S(0,-2), T(3,-6), U(4,-3) for triangle STU
A. PQ = ST: False, as the lengths of PQ and ST are different.
B. PQ = TU: False, as the lengths of PQ and TU are different.
C. ∠R = ∠U: False, as the angles R and U are not congruent.
D. ∠P = ∠U: False, as the angles P and U are not congruent.
E. QR = SU: False, as the lengths of QR and SU are different.
F. ∠Q = ∠T: True, as the angles Q and T are congruent.
So, the true statement is F: ∠Q = ∠T.