Final answer:
Rotation is a type of rigid motion where distances between object points remain constant. Congruency relates to rigid motion as it means shapes can be made to coincide by applying rigid motions like rotations without altering size or shape. The triangle congruence criteria (ASA, SAS, SSS) inherently follow this principle as they ensure identical relative measurements, enabling one triangle to map onto another through rigid motions, thus proving congruence.
Step-by-step explanation:
A rotation is a type of rigid motion where an object turns around a fixed point without changing its shape or size. All points in the object move in circular paths centered on one point. This is considered a rigid motion because distances between points in the object remain constant throughout the motion.
Congruency in geometric terms implies that one shape can become another using rigid motions which include rotations, reflections, and translations. Two figures are congruent if one can be moved on top of the other using these rigid motions, so that they match perfectly without altering their size or shape.
The criteria for triangle congruence (Angle-Side-Angle or ASA, Side-Angle-Side or SAS, Side-Side-Side or SSS) all follow from the definition of congruence in geometry. These criteria guarantee that if two triangles have three corresponding features that are identical, the triangles are congruent because they can be related by a series of rigid motions. There isn't a change in the relative measurements of the sides and angles of the triangle during these motions, proving congruence.