median of trapezoid
The segment connecting the midpoints of the legs (http://planetmath.org/Trapezoid) of a trapezoid, i.e. the median of the trapezoid, is parallel to the bases and its length equals the arithmetic mean of the legs.
Proof. Let and be the bases of a trapezoid and the midpoint of the leg and the midpoint of the leg . Then the median may be determined as vector as follows:
The last expression tells that and . Q.E.D.
Title | median of trapezoid |
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Canonical name | MedianOfTrapezoid |
Date of creation | 2013-03-22 17:46:44 |
Last modified on | 2013-03-22 17:46:44 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 6 |
Author | pahio (2872) |
Entry type | Theorem |
Classification | msc 51M04 |
Classification | msc 51M25 |
Related topic | MutualPositionsOfVectors |
Related topic | MidSegmentTheorem |
Related topic | TriangleMidSegmentTheorem |
Related topic | HarmonicMeanInTrapezoid |