Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.)
answer
$overline{km}$ is a perpendicular bisector.
$overline{km}$ is an angle bisector.
$m$ is the vertex of a right angle.
$k$ is the midpoint of a segment in the diagram.
$m$ is the midpoint of a segment in the diagram.
none of the above.

Explanation:

1. Analyze \(\overline{KM}\) as an angle bisector: The diagram shows equal arcs (or marks) at \(\angle JKL\) split by \(\overline{KM}\), so \(\overline{KM}\) divides \(\angle JKL\) into two equal angles, making it an angle bisector.
2. For \(\overline{KM}\) as a perpendicular bisector: There's no indication (like right angles or midpoint marks on another segment) that \(\overline{KM}\) is perpendicular to or bisects another segment (e.g., \(\overline{JL}\) isn't marked as bisected or perpendicular).
3. \(M\) as a right - angle vertex: The right angle is at \(J\), not \(M\), so this is false.
4. \(K\) as a midpoint: No segment is marked as having \(K\) as its midpoint (no midpoint symbol or indication of equal segments from \(K\) on a single segment).
5. \(M\) as a midpoint: No segment is marked as having \(M\) as its midpoint (no midpoint symbol or indication of equal segments from \(M\) on a single segment).

Answer:

\(\overline{KM}\) is an angle bisector.