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If hj is a median of Δikh, which of the following statements is always true?

1) The length of hj is equal to the length of ik
2) The length of hj is equal to the length of kh
3) The length of hj is half the length of ik
4) The length of hj is half the length of kh

User Chirael
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1 Answer

6 votes

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.

User Thordarson
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