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 2 out of 2 $overline{mn}$ is a segment bisector. $overline{mn}$ is a perpendicular bisector. $m$ is the vertex of a right angle. $n$ is the vertex of a right angle. $m$ is the midpoint of a segment in the diagram. $n$ is the midpoint of a segment in the diagram.

Explanation:

1. For \(\overline{MN}\) is a segment bisector: A segment bisector divides a segment into two equal parts. From the diagram, \(N\) and \(M\) are midpoints (as indicated by the tick marks on \(KL\) and \(JL\)), so \(MN\) connects midpoints, bisecting the sides, so this is true.
2. For \(\overline{MN}\) is a perpendicular bisector: A perpendicular bisector must be perpendicular (form a right angle) and bisect. The diagram doesn’t show \(MN\) forming a right angle with the sides, so this is false.
3. For \(M\) is the vertex of a right angle: There’s no indication (like a right - angle symbol) at \(M\), so this is false.
4. For \(N\) is the vertex of a right angle: There’s no right - angle symbol at \(N\), so this is false.
5. For \(M\) is the midpoint of a segment: The tick marks on \(JL\) show \(M\) divides \(JL\) into two equal parts, so \(M\) is the midpoint of \(JL\), this is true.
6. For \(N\) is the midpoint of a segment: The tick marks on \(KL\) show \(N\) divides \(KL\) into two equal parts, so \(N\) is the midpoint of \(KL\), this is true.

Answer:

\(\overline{MN}\) is a segment bisector, \(M\) is the midpoint of a segment in the diagram, \(N\) is the midpoint of a segment in the diagram.
(The false statements are \(\overline{MN}\) is a perpendicular bisector, \(M\) is the vertex of a right angle, \(N\) is the vertex of a right angle. But since the question asks for what must be true, we list the true ones: \(\overline{MN}\) is a segment bisector, \(M\) is the midpoint of a segment in the diagram, \(N\) is the midpoint of a segment in the diagram.)