select all that apply. (diagram is not to scale.)
answer attempt 2 out of 2
$ \overline { i m } $ is a perpendicular bisector.
$ i $ is the vertex of two angles that are congruent to one another.
$ i $ is the vertex of a right angle.
$ i $ is the midpoint of a segment in the diagram.
$ m $ is the midpoint of a segment in the diagram.
none of the above.

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Accepted Answer

# Brief Explanations:
1. For "$\overline{IM}$ is a perpendicular bisector": There's no indication of right angles or bisecting a segment at 90°, so this is false.
2. For "$I$ is the vertex of two angles that are congruent to one another": The diagram shows angle marks at $I$ and $M$ for angles formed by $IM$, suggesting $\angle LIM \cong \angle JIM$, so $I$ is the vertex of two congruent angles. This is true.
3. For "$I$ is the vertex of a right angle": No right angle symbol or indication, so false.
4. For "$I$ is the midpoint of a segment in the diagram": $I$ is a vertex, not a midpoint, so false.
5. For "$M$ is the midpoint of a segment in the diagram": $M$ is on $KL$, and visually (from the diagram's structure, though not to scale) it appears to be the midpoint of $KL$? Wait, no, the segment $KL$: but also, the key is the angle marks. Wait, actually, the position of $M$ on $KL$ – but the main correct one from the angle congruence. Wait, re - evaluating: The angle marks at $I$ (on $\angle JIM$ and $\angle LIM$) and at $M$ (on $\angle LIM$ and $\angle KIM$? No, the angle marks show that $\angle LIM$ and $\angle JIM$ (with $I$ as vertex) are congruent? Wait, the diagram has angle marks at $I$ (one mark) and at $M$ (one mark), meaning the angles at $I$ (formed by $JI$, $IM$ and $IM$, $LI$) and at $M$ (formed by $KM$, $IM$ and $IM$, $LM$) are congruent. Wait, no, the angle marks: if two angles have the same number of marks, they are congruent. So $\angle JIM \cong \angle LIM$ (both with one mark at $I$? Wait, the diagram shows one mark at $I$ (on the angle between $JI$ and $IM$) and one mark at $M$ (on the angle between $KM$ and $IM$)? No, maybe I misread. Wait, the correct one: "$I$ is the vertex of two angles that are congruent to one another" – because the angle marks indicate that the two angles with vertex $I$ (formed by $JI - IM$ and $IM - LI$) are congruent. And also, "$M$ is the midpoint of a segment in the diagram" – if $M$ is on $KL$ and the diagram's structure (even not to scale) suggests $M$ is the midpoint of $KL$? Wait, no, the key is the angle congruence first. But let's check again. The options: the first correct is "$I$ is the vertex of two angles that are congruent to one another" and also, is $M$ the midpoint? Wait, the segment $KL$: if $M$ is on $KL$ and the diagram (from the problem's diagram) – but maybe the main correct one is "$I$ is the vertex of two angles that are congruent to one another" and "$M$ is the midpoint of a segment in the diagram"? Wait, no, let's go back. The angle marks: at $I$, there's one mark (for $\angle JIM$) and at $M$, one mark (for $\angle LIM$? No, maybe the angle at $I$ (between $JI$ and $IM$) and the angle at $M$ (between $KM$ and $IM$) are congruent, but the option is about $I$ being the vertex of two congruent angles. So $\angle JIM$ and $\angle LIM$ (both with vertex $I$) are congruent (same angle mark). So that option is correct. Also, "$M$ is the midpoint of a segment in the diagram" – if $M$ is on $KL$, and the diagram (even not to scale) shows $M$ as the midpoint of $KL$ (since it's between $K$ and $L$ and the structure of the quadrilateral $JKLI$). But maybe the main correct ones are "$I$ is the vertex of two angles that are congruent to one another" and "$M$ is the midpoint of a segment in the diagram"? Wait, no, let's check the options again. The user's diagram: the quadrilateral is $JKLI$, with $M$ on $KL$. The angle marks: one at $I$ (on $\angle JIM$) and one at $M$ (on $\angle LIM$? No, maybe the angle at $I$ (between $JI$ and $IM$) and the angle at $M$ (between $KM$ and $IM$) are congruent, but the option is about $I$ having two congruent angles. So $\angle JIM \cong \angle LIM$ (vertex $I$), so that option is correct. And "$M$ is the midpoint of a segment in the diagram" – $M$ is on $KL$, so if $KL$ is a segment, $M$ is its midpoint (visually, as it's between $K$ and $L$ and the diagram's structure). But maybe the problem's correct options are "$I$ is the vertex of two angles that are congruent to one another" and "$M$ is the midpoint of a segment in the diagram". Wait, but let's re - check. The first option: $\overline{IM}$ is a perpendicular bisector – no. $I$ as right angle vertex – no. $I$ as midpoint – no. So the correct options are:

- $I$ is the vertex of two angles that are congruent to one another.
- $M$ is the midpoint of a segment in the diagram. (Assuming $M$ is the midpoint of $KL$ from the diagram's layout, even not to scale, as it's between $K$ and $L$ and the angle marks suggest symmetry around $IM$.)

But the main clear one is "$I$ is the vertex of two angles that are congruent to one another".
# Answer:
- $I$ is the vertex of two angles that are congruent to one another.
- $M$ is the midpoint of a segment in the diagram.

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