Unit Plan 20 (Grade 8 Math): Congruence via Rigid Motions
8th graders use sequences of rigid motions—translations, reflections, and rotations—to prove or disprove congruence between figures. They describe transformations precisely, track orientation, and justify congruence with clear reasoning.
Focus: Use sequences of rigid motions to argue congruence; determine if figures are congruent on the plane.
Grade Level: 8
Subject Area: Mathematics (Geometry)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week formalizes congruence using rigid motions (translations, reflections, rotations). Students decide whether two plane figures are congruent by exhibiting a sequence of rigid motions that maps one onto the other, attend to corresponding parts, and use clear, precise language to describe their sequences (order matters!). They also reason about orientation (whether a figure is mirrored) and explain why a proposed sequence proves congruence.
Essential Questions
- What does it mean for two figures to be congruent in Grade 8 terms?
- How can a sequence of rigid motions prove that two figures are congruent?
- How do orientation and correspondence affect the sequence I choose and how I describe it?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Define congruence via rigid motions: two figures are congruent if one can be carried onto the other by a sequence of translations, reflections, and/or rotations.
- Given two figures (on or off a grid), determine whether they are congruent by producing a specific sequence of rigid motions or explaining why no such sequence exists.
- Track and name corresponding points, sides, and angles and reason about orientation (reflections reverse orientation; translations/rotations preserve it).
- Communicate solutions with precise transformation language (vector, line of reflection, center/angle of rotation) and brief justifications.
Standards Alignment — CCSS Grade 8
- 8.G.2: Understand that two two-dimensional figures are congruent if one can be obtained from the other by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence.
Success Criteria (student-friendly)
- I can state a clear sequence (in order) that maps one figure to another.
- I can label corresponding parts and explain orientation differences.
- I can argue not congruent with a valid reason (for example, side lengths differ; no rigid motion matches).
- I can write my sequence with exact names: translation by a vector, reflection across a named line, rotation about a named center with a specified angle and direction.