Question

for \\( \triangle ghi \\) to the right, is the red dashed segment an altitude, a median, or neither? explain your answer.

choose the correct answer below
\\( \bigcirc \\) a. median, because it connects to the midpoint of a side.
\\( \bigcirc \\) b. neither, because it is perpendicular to one side and connects to the midpoint of the same side
\\( \bigcirc \\) c. altitude, because it is perpendicular to a side.
\\( \bigcirc \\) d. altitude, because it extends from a vertex of \\( \triangle ghi \\) and is perpendicular to the opposite side

Explanation:

An altitude of a triangle is a segment from a vertex perpendicular to the opposite side. A median is a segment from a vertex to the mid - point of the opposite side.
In the given triangle \( \triangle GHI\), the red - dashed segment starts from vertex \(H\) and is perpendicular to the opposite side \(GI\).
Option A is incorrect because there is no indication that the segment connects to the mid - point of the side.
Option B is incorrect as the segment is an altitude (not neither).
Option C is not fully correct as it does not mention the vertex - to - opposite - side relationship.
Option D correctly states that it is an altitude (since it extends from a vertex \(H\) of \( \triangle GHI\) and is perpendicular to the opposite side \(GI\)).

Answer:

D. Altitude, because it extends from a vertex of \( \triangle GHI\) and is perpendicular to the opposite side.