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.