Given is $\triangle PQR$ with altitudes $PS$ and $QT$. Prove that $ST$ is antiparallel with $PQ$.
What I've done up until now:
Given: $\triangle PQR$ with altitudes $QT$ and $PS$
What to prove: $P_1 = S_2$ (click here for the image)
I want to prove this with extremely basic mathematics, because my book solves this using the reverse of Thales' theorem, and cyclic quadrilaterals and such, and I believe there must be a simpler way to prove this, I however can't figure out how. Is there a simpler way?