Congruence Through Rigid Motions
Go from precise geometric definitions to proving triangles congruent with rigid motions, using only free resources.
Use rigid motions to decide and prove congruence
I can use the definition of congruence in terms of rigid motions to decide whether two figures are congruent, and to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
- Domain
- Geometry
- Level
- advanced
- Status
- draft · v0.1.0
- License
- CC BY-SA 4.0
Learn first
Learn it
Scope
Congruence defined through rigid motions, applied to deciding congruence of figures and to triangle congruence in terms of corresponding parts. The triangle congruence criteria (SSS, SAS, ASA) are the next outcome, currently a stub.
Resources
| Resource | Kind | Cost | Provider |
|---|---|---|---|
| Past Geometry Regents examinations | practice | free | New York State Education Department |
Courses that include it
Prove it
Evidence of mastery
- Given two figures, decides whether they are congruent and justifies the decision with a rigid motion or with an argument that none exists.
- Writes a proof that two triangles are congruent by exhibiting a sequence of rigid motions, and explains why corresponding parts are therefore congruent.
Assessments that measure it
Rigid Motion Congruence Task
A performance task in which the learner decides whether pairs of figures are congruent and proves it with rigid motions.
Credentials that include 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.
What comes next
- Prove triangles congruent with SSS, SAS, and ASA advanced stub
Alignments
- NYS Next Generation Mathematics Learning Standards:
GEO-G.CO.6 - NYS Next Generation Mathematics Learning Standards:
GEO-G.CO.7