Question

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

choose the correct answer below

o a. neither, because it is perpendicular to one side and connects to the midpoint of another side.
o b. median, because it connects to the midpoint of a side.
o c. altitude, because it extends from a vertex of △ghi and is perpendicular to the opposite side.
o d. altitude, because it is perpendicular to a side.

Explanation:

An altitude of a triangle is a segment from a vertex perpendicular to the opposite side. A median connects a vertex to the mid - point of the opposite side.
In the given triangle, the red dashed segment extends from a vertex (vertex \(G\)) and is perpendicular to the opposite side (\(HI\)).
Option A is incorrect because being perpendicular to one side and connecting to the mid - point of another side is not a standard property of altitude or median.
Option B is incorrect as it is not connecting to the mid - point of a side (no indication of mid - point in the given figure).
Option D is incorrect because just being perpendicular to a side is not sufficient (it should be from a vertex to the opposite side).

Answer:

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