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In proposition 29, we prove that if two parallel lines are intersected by a third line, then the alternate interior angles, are congruent, the exterior angle is congruent to the opposite interior angle, and the sum of two interior angles on the same side are congruent to the sum of two right angles.
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(I.29) Proposition 29, Euclid's Elements
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Euclidgreekproofmathematicselementselementoseuclid'sgeometryLincolneuclideseuklidplanestraightedgecompassMathaxiomspostulatesdefinitionspropositionaxiomEuclideannon-euclideancongruentequalanglegreater thanlessshapesbeginningscoincideglobalclassroomedugurubasealternate interiorexterior angleparallel linesfifth postulate