Final answer:
The correct distinction between medians and altitudes of a triangle is that medians connect each vertex to the midpoint of the opposite side, while altitudes are perpendicular lines from vertices to the opposite sides.
Step-by-step explanation:
The correct answer to the question is option (a): Medians are lines drawn from each vertex to the midpoint of the opposite side; altitudes are lines drawn from each vertex perpendicular to the opposite side. To further clarify, a median of a triangle connects a vertex of the triangle to the midpoint of the opposite side, effectively dividing the side into two equal segments. There are three medians in a triangle, and they intersect each other at the triangle's centroid, which is the center of mass or balance point of the triangle. An altitude of a triangle, on the other hand, is a line segment drawn from a vertex perpendicular to the side opposite that vertex (or an extension of that side). Altitudes may lie inside or outside the triangle depending on the type of triangle. There are also three altitudes in a triangle, and they intersect at a point called the orthocenter.