Congruence Through Rigid Motions
Go from precise geometric definitions to proving triangles congruent with rigid motions, using only free resources.
Rigid Motion Congruence Task
A performance task in which the learner decides whether pairs of figures are congruent and proves it with rigid motions.
- Kind
- performance-task
- Status
- draft · v0.1.0
- License
- CC BY-SA 4.0
Outcomes measured
- Describe and draw rotations, reflections, and translations
- Use rigid motions to decide and prove congruence
Evidence required
- A portfolio of five figure pairs, at least two congruent and at least two not, designed by the learner.
- For each congruent pair, an explicit sequence of rigid motions carrying one figure onto the other, drawn and described.
- For each non-congruent pair, an explanation of why no rigid motion can exist.
- One written proof that two given triangles are congruent, concluding that corresponding parts are congruent.
Task
You will be given two pairs of figures by the assessor and will add three pairs of your own. For every pair, decide whether the figures are congruent. Justify each decision: with a sequence of rigid motions if they are congruent, and with an argument that no rigid motion can exist if they are not. Finish with a proof for one pair of triangles that their corresponding sides and angles are congruent.
Scoring guide
| Level | Description |
|---|---|
| Proficient | Every decision is correct. Every congruent pair has a correct, complete sequence of rigid motions. The triangle proof is valid and uses the definition of congruence in terms of rigid motions. |
| Developing | Decisions are correct but at least one justification is incomplete or relies on appearance rather than a rigid motion. |
| Beginning | At least one decision is incorrect, or justifications do not use rigid motions. |
Only Proficient work counts as evidence for the Congruence and Rigid Motions credential.
Free instruments
Past New York State Geometry Regents examinations, published with answer keys and rating guides at nysedregents.org, contain questions aligned to the same standards and can be used for additional practice or as supplementary evidence.
Where this assessment is used
Courses that prepare for it
Credentials that require it
Congruence and Rigid Motions
The holder can define the objects of plane geometry, represent and perform rigid motions, and prove figures congruent using rigid motions.