Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.)$ik$ is a segment bisector.$ik$ 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. $IK$ is a segment bisector: A segment bisector divides a segment into two congruent parts. The diagram shows $KL$ is split into two congruent segments by $K$? No, $IK$ connects to $K$, and $KL$ has marks showing $K$ is not the midpoint. Wait, no: The marks on $IL$ show $IK$ splits $IL$ into two congruent parts, so $IK$ bisects $IL$. This is true.
2. $IK$ is an angle bisector: An angle bisector splits an angle into two congruent angles. The diagram has marks showing $IK$ splits $\angle JIL$ into two congruent angles, so this is true.
3. $K$ is the vertex of two congruent angles: There are no marks indicating angles at $K$ are congruent, so this is not necessarily true.
4. $I$ is the midpoint of a segment: $I$ is an endpoint of $JI$ and $IL$; it does not split any segment into two congruent parts, so this is false.
5. $K$ is the midpoint of a segment: $K$ is an endpoint of $JK$ and $KL$; the marks on $KL$ show $K$ is not the midpoint, so this is false.

Answer:

• $IK$ is a segment bisector.
• $IK$ is an angle bisector.