KnowraMidpoint theoremMidpoint theoremIn a triangle, the segment joining the midpoints of two sides is parallel to the third side and half its length.BriefConnectTriangle similarity: A relation between triangles that have equal corresponding angles and proportional corresponding side lengths. A smaller triangle formed by the midpoint segment is similar to the original triangle.Midpoint: The point halfway between two endpoints of a line segment. The theorem begins by selecting the halfway point on each of two triangle sides.Triangle midsegment: A segment joining the midpoints of two sides of a triangle. It is the specific segment whose direction and length the theorem determines.Midpoint theorem converse: A converse stating that a line through the midpoint of one triangle side, parallel to another side, bisects the third side. It reverses the theorem’s setup and conclusion about a midpoint and parallel line.Thales' theorem: A theorem stating that a line parallel to one side of a triangle divides the other two sides proportionally. A parallel-line proportion gives a direct route to the midpoint relationship.Line segment: The part of a line bounded by two endpoints, including every point between them. The theorem compares the segment joining two midpoints with a triangle’s third side.Trapezoid midsegment: A segment joining the midpoints of the nonparallel sides of a trapezoid; its length is the average of the bases. Splitting a trapezoid along a diagonal reduces its midsegment relation to triangle midpoint results.Median (geometry): A segment joining a triangle vertex to the midpoint of the opposite side. A median also uses a side midpoint, but starts at a vertex rather than joining two midpoints.Intercept theorem: A theorem that parallel lines cut transversals in proportional segments. It explains why bisecting two sides forces the joining segment to be parallel to the third.Parallel lines: Coplanar lines that never intersect, however far they are extended. Parallelism is the theorem’s key directional conclusion.Show all 20Linked from 1 pageSegment Addition PostulateRelated: Its midpoint relationships rely on comparing and combining lengths of segments.