Rigid Motion Congruence Task
A performance task in which the learner decides whether pairs of figures are congruent and proves it with rigid motions.
Congruence Through Rigid Motions
Go from precise geometric definitions to proving triangles congruent with rigid motions, using only free resources.
- Domain
- Geometry
- Estimated time
- About 12 hours
- Formats
- video, interactive, practice, project
- Cost
- Free
- Status
- draft · v0.1.0
- License
- CC BY-SA 4.0
Outcomes you will reach
- Define the basic objects of plane geometry foundation
- Represent transformations in the plane foundation
- Describe and draw rotations, reflections, and translations intermediate
- Use rigid motions to decide and prove congruence advanced
Resources
| Resource | Kind | Cost | Provider |
|---|---|---|---|
| Khan Academy, High School Geometry | video | free | Khan Academy |
| GeoGebra Geometry | tool | free | GeoGebra |
| NYS Next Generation Mathematics Learning Standards (P-12) | reference | free | New York State Education Department |
| Past Geometry Regents examinations | practice | free | New York State Education Department |
Plan
Step 1: Definitions
Outcome: Define the basic objects of plane geometry.
Work through the definitions of angle, circle, perpendicular lines, parallel lines, and line segment. Write each definition in your own words using only point, line, distance along a line, and distance around a circular arc. Test each definition against figures in GeoGebra: can you find something your definition accepts that it should not?
Step 2: Transformations as functions
Outcome: Represent transformations in the plane.
Build a transformation in GeoGebra, drag the input point, and watch the output. Describe each transformation as a rule that takes a point and returns a point. Sort translations, rotations, reflections, dilations, and stretches by whether they preserve distance and angle.
Step 3: Rigid motions
Outcome: Describe and draw rotations, reflections, and translations.
Define each rigid motion precisely. Practice drawing images by hand and in software. Given two congruent figures, find a sequence of rigid motions that carries one onto the other, then find a shorter one.
Step 4: Congruence
Outcome: Use rigid motions to decide and prove congruence.
Use rigid motions to decide whether pairs of figures are congruent. Prove that congruent triangles have congruent corresponding parts, and that congruent corresponding parts imply a rigid motion exists.
Project
Build a congruence portfolio: five pairs of figures of your own design, a rigid-motion argument for each congruent pair, and a written explanation for each non-congruent pair. This portfolio is the evidence for the course’s assessment.
Check your progress
Complete the Rigid Motion Congruence Task. Past Regents examinations are a free source of additional practice questions aligned to the same standards.