Final answer:
The statement is true; the Side-Side-Side (SSS) congruence theorem is used to establish the congruence of two triangles with three pairs of congruent sides. It's an essential part of Euclidean geometry for proving triangles are identical in size and shape through comparing side lengths.
Step-by-step explanation:
The statement is true: when all three sides of one triangle are congruent to all three sides of another triangle, this principle is known as the Side-Side-Side (SSS) congruence theorem. This theorem is a fundamental principle in Euclidean geometry which is used to determine when two triangles are congruent, meaning they have the same size and shape, regardless of their orientation or position.
Triangles are three-sided polygons where the sum of the interior angles always adds up to 180 degrees. The SSS congruence theorem is one of several congruence criteria that include Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS), each serving as a method to prove congruence between two triangles.
The SSS congruence rule requires no knowledge of angles, relying solely on the lengths of sides. This distinction of congruence rules is crucial in geometric proofs and solving for unknown geometrical values, following the logical notion that if quantifiable aspects of two objects are equal, then the objects themselves are equal.