Question

if rs=st then point s is called the midpoint of (overline{rt}). (\bigcirc) always (\bigcirc) sometimes (\bigcirc) never

Explanation:

To be the midpoint of \(\overline{RT}\), point \(S\) must lie on \(\overline{RT}\) and \(RS = ST\). If \(RS = ST\) but \(S\) is not on \(\overline{RT}\) (e.g., forming an isosceles triangle with \(R\) and \(T\)), then \(S\) is not the midpoint. However, if \(S\) is on \(\overline{RT}\) and \(RS = ST\), then it is the midpoint. So the condition \(RS = ST\) means \(S\) is the midpoint of \(\overline{RT}\) only in some cases (when \(S\) is collinear with \(R\) and \(T\)).

Answer:

sometimes