Question

select the three statements that guarantee $overleftrightarrow{st}$ is the perpendicular bisector to $uv$. show your work here $overline{sw}congoverline{uv}$ $overline{sv}congoverline{tv}$ $overline{ut}congoverline{sv}$ $overline{uv}congoverline{st}$ $overline{us}congoverline{ut}$ $overline{tw}congoverline{vw}$ $overline{sw}congoverline{uw}$

Explanation:

Step1: Recall perpendicular - bisector properties

A line is the perpendicular bisector of a segment if any point on the line is equidistant from the endpoints of the segment.

Step2: Analyze each option

• If $\overline{US}\cong\overline{UT}$, point $U$ is equidistant from $S$ and $T$.
• If $\overline{SV}\cong\overline{TV}$, point $V$ is equidistant from $S$ and $T$.
• If $\overline{SW}\cong\overline{UW}$, point $W$ (the mid - point of $\overline{UV}$) is equidistant from $S$ and $U$. This helps in showing that $ST$ is perpendicular to $UV$ and bisects it.

Answer:

$\overline{US}\cong\overline{UT}$, $\overline{SV}\cong\overline{TV}$, $\overline{SW}\cong\overline{UW}$