Propositions from Book 1

Proposition: Sum Of Angles in a Triangle and Exterior Angle

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(Proposition 32 from Book 1 of “Euklid’s Elements”)

In any triangle \(\triangle{ABC}\), if one of the sides is extended (without loss of generality extend segment \(AB\) to segment \(BD\)) is extended, then:

1. the exterior angle equals the sum of the its interior and opposite angles:
   \[\angle{DBC}=\angle{ACB}+\angle{BAC}.\]
2. the sum of the three interior angles of the triangle equals two right angles;
   \[\angle{CBA}+\angle{ACB}+\angle{BAC}=\text{two right angles}.\]

References

[628] Casey, John: “The First Six Books of the Elements of Euclid”, http://www.gutenberg.org/ebooks/21076, 2007
[626] Callahan, Daniel: “Euclid’s ‘Elements’ Redux”, http://starrhorse.com/euclid/, 2014

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