Pythagorean Theorem – Geometric Proof

Right triangle ABC with right angle at B; altitude from B to hypotenuse AC; similar sub-triangles; area scaling.
a² b² c² A B C H a = |AB| b = |BC| c = |AC| [ABC] [AHB] [BHC]
Welcome
Use Play/Next to step through the geometric proof.
Goal: prove c² = a² + b² with area partition and similar triangles.
Step index
  1. Triangle setup (right angle at B)
  2. Label sides a, b, c
  3. Draw altitude BH to hypotenuse AC
  4. Sub-triangles AHB and BHC partition area
  5. Similarity: △ABC ~ △AHB ~ △BHC
  6. Area ratios scale as square of side ratios
  7. Conclude c² = a² + b²