Which of the following does not always bisect at least one side?

Mid segment,Perpendicular bisector, Median,Altitude

To determine which of the following does not always bisect at least one side, we need to understand what each term means.

1. Midsegment: A midsegment of a triangle connects the midpoints of two sides. It always bisects the third side of the triangle.

2. Perpendicular Bisector: A perpendicular bisector of a line segment is a line that divides the segment into two equal parts, while also being perpendicular to the line segment. In the case of a triangle, the perpendicular bisector meets the side at a right angle, dividing it into two equal segments.

3. Median: A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. It always bisects the side it connects to.

4. Altitude: An altitude is a line segment drawn from a vertex perpendicular to the opposite side or an extension of it. It may or may not bisect the side depending on the type of triangle.

Based on the explanations, we can conclude that the "altitude" does not always bisect at least one side. In scalene triangles, the altitude can intersect the opposite side at a point that is not the midpoint, thus not bisecting the side. However, in isosceles triangles, the altitude will bisect the base (the side opposite the equal sides).

Therefore, the correct answer is "Altitude." It is the only option that does not always bisect at least one side.