triangle mid-segment theorem
Theorem. The segment connecting the midpoints of any two sides of a triangle is parallel to the third side and is half as long.
Proof. In the triangle , let be the midpoint of and the midpoint of . Using the side-vectors and as a basis (http://planetmath.org/Basis) of the plane, we calculate the mid-segment as a vector:
The last expression indicates that the segment is such as asserted.
Corollary (Varignon’s theorem). If one connects the midpoints of the of a quadrilateral, one obtains a parallelogram.
Title | triangle mid-segment theorem |
Canonical name | TriangleMidsegmentTheorem |
Date of creation | 2013-03-22 17:46:35 |
Last modified on | 2013-03-22 17:46:35 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 12 |
Author | pahio (2872) |
Entry type | Theorem |
Classification | msc 51M04 |
Classification | msc 51M25 |
Synonym | mid-segment theorem |
Related topic | MutualPositionsOfVectors |
Related topic | ParallelogramTheorems |
Related topic | MedianOfTrapezoid |
Related topic | CommonPointOfTriangleMedians |
Related topic | Grafix |
Related topic | SimonStevin |
Related topic | InterceptTheorem |