Why the midsegment of a trapezoid is always the average of its bases
In short: This video demonstrates the geometric proof behind a fundamental trapezoid property: the segment connecting the midpoints of the non-parallel sides is exactly half the sum of the top and bottom bases. It is a clear look at how triangle congruence and similarity reveal hidden relationships in shapes.
The midsegment of a trapezoid acts as a bridge between its two parallel sides. By applying principles of congruent and similar triangles, we can verify that its length is consistently the arithmetic mean of the two bases. This relationship remains valid regardless of whether you classify a trapezoid as having a single pair of parallel sides or at least one pair.
Understanding this proof helps solidify how basic geometric properties build upon one another. By breaking down the trapezoid into triangles, the logic behind the midsegment formula becomes intuitive rather than just a rule to memorize.
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Sources
- Summary by Intellect · source: Proof: Trapezoid midsegment length | Geometry (FL B.E.S.T.) | Khan Academy
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