What is the segment connecting the midpoints of two sides of a triangle, parallel to the third side and measuring half its length?

The segment connecting the midpoints of two sides of a triangle is known as the midsegment of a triangle. This midsegment has two significant properties: it is parallel to the third side of the triangle and its length is exactly half the length of that third side.

To visualize this, consider a triangle with vertices A, B, and C. If points D and E are the midpoints of sides AB and AC, respectively, then segment DE is the midsegment. According to the triangle midsegment theorem, segment DE will be parallel to side BC and will measure half of BC's length. This relationship helps in various geometric proofs and constructions and can also be used to simplify calculations involving triangles.

In contrast, the other options refer to different constructions in geometry. The altitude is a segment from a vertex perpendicular to the opposite side, the median connects a vertex to the midpoint of the opposite side, and the perpendicular bisector is a line that divides a segment into two equal parts at a right angle. Each of these serves a different purpose in triangle geometry and does not share the properties of the midsegment.