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SSS postulate

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In geometry, the SSS postulate ("SSS" being short for "side, side, side") is a postulate stating that when two triangles have corresponding sides equal in length, then the two triangles are congruent. It is one of the several ways to prove two triangles congruent.

More precisely, the postulate is as follows. Let two triangles ABC and XYZ be given. If segment AB is congruent to segment XY, and segment BC is congruent to segment YZ, and segment AC is congruent to segment XZ, then the triangles ABC and XYZ are congruent (and thus have corresponding angles equal in size).

The SSS postulate corresponds closely to Proposition 8 in Book 1 of Euclid's Elements. It is normally regarded as given in modern geometric proofs.

References

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