MathematicsGeneralQuality 60 · Exceptional

The Pythagorean Theorem and Why It Works

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Kai Brennan Verified Teacher
@author · 2026-06-27 · 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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Omar H.
16 days ago
The step-by-step is what makes this work. Most explanations skip that.
Lena F. Teacher
16 days ago
Thanks for the kind words! Happy it helped.
Dr. Tan
16 days ago
The intuition you build before the formal definition is everything.
Marcus B.
16 days ago
Bookmarked. Coming back to this before the exam.