Key Concepts: Congruence Transformations

Rigid Motions (Isometries)

A transformation that preserves distance and Angle measure is called a rigid motion or isometry. Rigid motions produce congruent figures.

Three Types of Rigid Motions

• Translation: Slides a figure in a given direction by a given distance. Every Point moves the same distance.
• Reflection: Flips a figure over a Line (Line of reflection). Each Point is the same distance from the Line on the opposite side.
• Rotation: Turns a figure around a fixed Point (center of rotation) by a given Angle.

Key Properties

• All three rigid motions preserve side lengths, Angle measures, and parallelism.
• The pre-image and image are always congruent.
• Compositions of rigid motions (doing two or more in sequence) also produce congruent figures.