Question

(angle swt) is a right angle and (overline{vw} cong overline{sw}).
which term describes (overline{tw})?

• angle bisector
• perpendicular bisector
• altitude
• median

Explanation:

1. First, recall the definitions:

• An angle bisector splits an angle into two equal angles.
• A perpendicular bisector is a line perpendicular to a segment that passes through its midpoint.
• An altitude is a segment from a vertex perpendicular to the opposite side (or its extension).
• A median is a segment from a vertex to the midpoint of the opposite side.

1. We know $\overline{VW} \cong \overline{SW}$, so $W$ is the midpoint of $\overline{SV}$.
2. Segment $\overline{TW}$ connects point $T$ to $W$, the midpoint of the opposite side $\overline{SV}$ of triangle $STU$. This matches the definition of a median.

(Note: $\angle SWT$ being a right angle is not relevant to the definition of $\overline{TW}$ here, as $TW$ is not perpendicular to a side of the larger triangle $STU$.)

Answer:

median