Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.)

$overline{gh}$ is a segment bisector.
$overline{gh}$ is a perpendicular bisector.
$g$ is the vertex of a right angle.
$h$ is the vertex of a right angle.
$h$ is the midpoint of a segment in the diagram.

Explanation:

1. For \(\overline{GH}\) being a segment bisector: The marks on \(ED\) show \(G\) is the midpoint, and \(GH\) passes through \(G\) (midpoint) of \(ED\), so it bisects \(ED\), so this is true.
2. For \(\overline{GH}\) being a perpendicular bisector: \(GH\) is perpendicular to \(ED\) (right angle at \(G\)) and bisects \(ED\) (since \(G\) is midpoint), so this is true.
3. For \(G\) being the vertex of a right angle: The diagram has a right angle symbol at \(G\) between \(GH\) and \(ED\), so \(\angle HGD\) (or \(\angle HGE\)) is right, so \(G\) is the vertex, true.
4. For \(H\) being the vertex of a right angle: The right angle is at \(G\), not \(H\), so false.
5. For \(H\) being the midpoint: There's no indication \(H\) bisects any segment, so false.

Answer:

• \(\overline{GH}\) is a segment bisector.
• \(\overline{GH}\) is a perpendicular bisector.
• \(G\) is the vertex of a right angle.