Question

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
$overline{ik}$ is a segment bisector.
$overline{ik}$ is an angle bisector.
$k$ is the vertex of two angles that are congruent to one another.
$i$ is the midpoint of a segment in the diagram.
$k$ is the midpoint of a segment in the diagram.
none of the above.

Explanation:

1. $\overline{IK}$ is a segment bisector: A segment bisector divides a segment into two congruent parts. $\overline{IK}$ does not split any marked segment into two equal parts, so this is false.
2. $\overline{IK}$ is an angle bisector: An angle bisector splits an angle into two congruent angles. The diagram shows $\overline{IK}$ divides $\angle JKL$ into two congruent angles (marked with the same symbol), so this is true.
3. $K$ is the vertex of two angles that are congruent to one another: The two angles at vertex $K$ formed by $\overline{IK}$ are marked as congruent, so this is true.
4. $I$ is the midpoint of a segment in the diagram: $I$ is an endpoint of $\overline{JI}$ and $\overline{IL}$; $\overline{IL}$ has congruent segments from $I$ to the marked point, but $I$ is not a midpoint of any segment, so this is false.
5. $K$ is the midpoint of a segment in the diagram: $K$ is an endpoint of $\overline{JK}$ and $\overline{KL}$, and is not the midpoint of any segment, so this is false.

Answer:

$\overline{IK}$ is an angle bisector.
$K$ is the vertex of two angles that are congruent to one another.