Final answer:
None of the statements provided about the lengths of hj in relation to ik or kh are always true just because hj is a median of Δikh. Additional information about the triangle would be required to ascertain any relationships between these lengths.
Step-by-step explanation:
If hj is a median of Δikh, then by definition, it is a line segment drawn from vertex h to the midpoint j of the opposite side ik. A median does not necessarily have a relationship to the lengths of the sides of the triangle in terms of equality or proportionality unless specific conditions are satisfied, which are not given here.
This means that:
- The length of hj is not necessarily equal to the length of ik.
- The length of hj is not necessarily equal to the length of kh.
- The length of hj is not necessarily half the length of ik.
- The length of hj is not necessarily half the length of kh.
Therefore, none of the provided statements are always true just because hj is a median. To make any of these statements accurate, additional information about the sides of the triangle or angles would be needed.