Question 763284
I'm not able to draw a picture for the problem, but here is the solution.

Consider the 2 triangles RQS and TUS

RQ = TU (given)
SQ = SU (since QSU is an isosceles triangle)
Angle RQS = Angle TUS (given)

Thus we see that 2 sides and the included angle in the 2 triangles are equal. Hence, by the Side-Angle-Side (SAS) theorem, the 2 triangles are congruent.

Therefore, RS = ST (corresponding sides of congruent triangles)

And so, S is the midpoint of RT.

:)