In geometry, the crossbar theorem states that if ray AD is between ray AC and ray AB, then ray AD intersects line segment BC. This result is one of the deeper results in axiomatic plane geometry. It is often used in proofs to justify the statement that a line through a vertex of a triangle lying inside the triangle meets the side of the triangle opposite that vertex. This property was often used by Euclid in his proofs without explicit justification.
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