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 2 out of 2
$overline{st}$ is a segment bisector.
$overline{st}$ is an angle bisector.
$s$ is the vertex of two angles that are congruent to one another.
$s$ is the midpoint of a segment in the diagram.
$t$ is the midpoint of a segment in the diagram.
none of the above.

Explanation:

1. Segment bisector check: $\overline{ST}$ splits $\overline{QR}$ into two marked congruent segments, so $T$ is the midpoint of $\overline{QR}$, making $\overline{ST}$ a segment bisector.
2. Angle bisector check: The marks at vertex $S$ show the two angles formed by $\overline{ST}$ are congruent, so $\overline{ST}$ is an angle bisector.
3. Congruent angles at $S$: The angle marks at $S$ confirm the two angles with vertex $S$ are congruent.
4. Midpoint check for $S$: $S$ is a vertex of the triangle, not a midpoint of any segment in the diagram.
5. Midpoint check for $T$: The marks on $\overline{QR}$ show $QT=TR$, so $T$ is the midpoint of $\overline{QR}$.

Answer:

• $\overline{ST}$ is a segment bisector.
• $\overline{ST}$ is an angle bisector.
• $S$ is the vertex of two angles that are congruent to one another.
• $T$ is the midpoint of a segment in the diagram.