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

$overline{wx}$ is a segment bisector.
$overline{wx}$ is a perpendicular bisector.
$overline{wx}$ is an angle bisector.
$w$ is the vertex of two angles that are congruent to one another.
$w$ is the vertex of a right angle.

Explanation:

1. For \(\overline{WX}\) being a segment bisector: From the diagram, \(W\) bisects \(VU\) (marked with equal segments) and \(X\) bisects \(UT\) (marked with equal segments), so \(\overline{WX}\) divides segments, making it a segment bisector.
2. For \(W\) being the vertex of two congruent angles: Since \(VW = WU\) (marked equal), triangle \(VWU\) is isosceles with \(\angle WVU\cong\angle WUV\), so \(W\) is the vertex of two congruent angles.
3. \(\overline{WX}\) is not a perpendicular bisector (no right - angle mark or indication of perpendicularity).
4. \(\overline{WX}\) is not an angle bisector (no indication of angle division).
5. \(W\) is not the vertex of a right angle (no right - angle mark).

Answer:

\(\overline{WX}\) is a segment bisector.
\(W\) is the vertex of two angles that are congruent to one another.