Unit 3 · Transformations

3.7Rigid Motions and Congruence

Quick Answer

Two figures are congruent if and only if there exists a sequence of rigid motions (translations, reflections, rotations) that maps one onto the other. This is the transformation-based definition of congruence.

Essential Question

How does the concept of rigid motion provide a precise, transformation-based definition of congruence?

Learning Goals

  • 1State the transformation-based definition of congruence.
  • 2Describe a sequence of rigid motions that maps one figure onto another.
  • 3Prove figures congruent by identifying a rigid motion sequence.
  • 4Connect rigid motion congruence to the traditional CPCTC definition.

Key Vocabulary

Congruence (transformation definition)

Two figures are congruent if and only if one can be mapped onto the other by a sequence of rigid motions.

Rigid motion sequence

A series of translations, reflections, and/or rotations applied in order.

Full lesson content coming soon

Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.