In right-angled triangles, the square on the side subtending the right angle is equal to the (sum of the) squares on the sides containing the right angle.

- Let $ABC$ be a right-angled triangle having the angle $BAC$ a right angle.
- I say that the square on $BC$ is equal to the (sum of the) squares on $BA$ and $AC$.

In a right triangle (\(\triangle{ABC}\)), the square on the hypotenuse (\(\overline{BC}\)) is equal to the sum of the squares on the other two sides (\(\overline{AB}\), \(\overline{CA}\)).

This theorem is also known as the theorem of Pythagoras.

| | | | | created: 2014-10-05 18:25:43 | modified: 2019-03-24 08:10:46 | by: *bookofproofs* | references: [626], [628], [6419]

[626] **Callahan, Daniel**: “Euclid’s ‘Elements’ Redux”, http://starrhorse.com/euclid/, 2014

[6419] **Fitzpatrick, Richard**: “Euclid’s Elements of Geometry”, http://farside.ph.utexas.edu/Books/Euclid/Euclid.html, 2007

[628] **Casey, John**: “The First Six Books of the Elements of Euclid”, http://www.gutenberg.org/ebooks/21076, 2007

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