Proposition: 1.48: The Converse of the Pythagorean Theorem
(Proposition 48 from Book 1 of Euclid's “Elements”)
If the square on one of the sides of a triangle is equal to the (sum of the) squares on the two remaining sides of the triangle then the angle contained by the two remaining sides of the triangle is a right angle.
 For let the square on one of the sides, $BC$, of triangle $ABC$ be equal to the (sum of the) squares on the sides $BA$ and $AC$.
 I say that angle $BAC$ is a right angle.
Modern Formulation
If the square on one side (\(\overline{BC}\)) of a triangle (\(\triangle{ABC}\)) equals the sum of the squares on the remaining sides (\(\overline{BA}\), \(\overline{AC}\)), then the angle (\(\angle{CAB}\)) opposite to that side is a right angle.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1
Sections: 2
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References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"