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MathematicsGeneralQuality 66 · Exceptional

The Pythagorean Theorem and Why It Works

PR
Zara RodriguezTeacher Tier
@author · 2026-08-21 · v1
7 min read
In a right triangle,
a2+b2=c2a^2 + b^2 = c^2
. Rearranging four copies of the triangle into a large square proves it visually: the inner square has side
cc
, and the four triangles plus the inner square fill a square of side
a+ba+b
, so
c2=(a+b)2−2(12ab)=a2+b2c^2 = (a+b)^2 - 2(\frac{1}{2}ab) = a^2 + b^2
.
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