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Why are all right angles considered equal in Euclidean geometry?
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Euclidean geometry
This diagram depicts three basic theorems that triangles are congruentâthat is, they are of equal shape and sizeâif: (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 statement that all right angles are equal is not a theorem that requires a proof; rather, it is one of the five fundamental axioms (or postulates) proposed by Euclid in his work, the Elements.1
Euclid established these axioms as intuitive, self-evident principles that serve as the logical foundation for all subsequent geometric deductions. Because this principle is defined as an axiom, it is accepted as a starting point for the system rather than something derived from other geometric properties.1