Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.)
answer attempt 1 out of 2
$overline{st}$ is a segment bisector.
$overline{st}$ is a perpendicular bisector.
$t$ is the vertex of two angles that are congruent to one another.
$t$ is the vertex of a right angle.
$s$ is the midpoint of a segment in the diagram.
$t$ is the midpoint of a segment in the diagram.

Explanation:

Step1: Analyze segment bisector $\overline{ST}$

$\overline{ST}$ splits $\overline{RP}$ into two congruent segments (marked by ticks), so it bisects $\overline{RP}$. Also, $\overline{ST} \perp \overline{RP}$ (right angle mark).

Step2: Check midpoint S

The ticks on $\overline{RS}$ and $\overline{SP}$ show $RS=SP$, so $S$ is the midpoint of $\overline{RP}$.

Step3: Check midpoint T

The ticks on $\overline{RT}$ and $\overline{TQ}$ show $RT=TQ$, so $T$ is the midpoint of $\overline{RQ}$.

Step4: Check angle at T

There is no indication of congruent angles with vertex $T$, nor a right angle at $T$.

Step5: Verify perpendicular bisector

$\overline{ST}$ is perpendicular to $\overline{RP}$ and bisects it, so it is a perpendicular bisector of $\overline{RP}$. It is also a segment bisector (since it bisects $\overline{RP}$).

Answer:

$\overline{ST}$ is a segment bisector.
$\overline{ST}$ is a perpendicular bisector.
$S$ is the midpoint of a segment in the diagram.
$T$ is the midpoint of a segment in the diagram.