Why can a line segment be extended indefinitely in Euclidean geometry?

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Three theorems of congruent triangles — Euclidean geometry This diagram depicts three basic theorems that triangles are congruent—that is, they are of equal shape and size—if: (1) two sides and the included angle are equal, designated SAS; (2) two angles and the included side are equal, designated ASA; or (3) all three sides are equal, designated SSS.

In Euclidean geometry, the ability to extend a line segment indefinitely is not a derived property, but rather a foundational principle established by Euclid as one of his five axioms (or postulates).1

Specifically, the second postulate states that a straight line segment can be prolonged indefinitely. This axiom serves as a fundamental rule for logical deduction within the system, allowing mathematicians to define lines as extensions of segments. By accepting this principle as an unprovable but intuitive starting point, Euclid provided the necessary framework to build the theorems and geometric structures that define his system.12