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This is the fourth proposition in Euclid's first book of The Elements. This proof effectively shows that when you have two triangles, with two equal sides and the angles between those sides are equal, then the two triangles are exactly equal. In modern day terms, this is known as the side angle side (S.A.S.) theorem.
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Euclid's Elements Book 1: Proposition 4, Side Angle Side Theorem | NatokHD