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Q: What is the segment of a triangle joining a vertex in the midpoint of the side opposite the vertex?

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A triangle is not a segment joining a vertex and the midpoint of the side opposite the vertex.

Median

Median

Median

A median of a triangle is a line or segment that passes through a vertex and the midpoint of the side opposite that vertex. The median only bisects the vertex angle from which it is drawn when it is an isosceles triangle.

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A triangle is not a segment joining a vertex and the midpoint of the side opposite the vertex.

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side.

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Altitude of a triangle is a straight line through a vertex and perpendicular to the opposite side or an extension of the opposite side.

Median

Median

Median

The triangle midpoint theorem states that the line segment is parallel to the third side and is congruent to one half of the third side.

Median

Median

Assuming that you meant midpoint, it is a median.

median

The midpoint theorem says the following: In any triangle the segment joining the midpoints of the 2 sides of the triangle will be parallel to the third side and equal to half of it