# 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.

Proofs: 1

Proofs: 1
Sections: 2

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### References

#### Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014