The Pythagorean Proposition: Geometric Proofs, Proof #31

Thirty-One

Fig. 132

Extend GA making AP
= AG; extend DB making BN
= BD = CP.  Tri. CKP = tri. ANB = ½ sq. HD = ½ rect. LK.
Tri. APB = ½ sq. HG = ½ rect. AM.  Sq. AK = rect. AM
+ rect. LK.

∴ sq. upon AB = sq. upon HB + sq. upon AH.  ∴ h² = a² + b².  Q.E.D.

a. This is Huygens' proof (1657); see also Ver­sluys, p. 25, fig. 22.