📐 Geometry

Reasoning about shapes, transformations, and congruence in the plane, from precise definitions to proof.

Outcomes

4 written · 1 stub

Status

draft · v0.1.0

License

CC BY-SA 4.0

Geometry is the first seed domain because it has a clear prerequisite structure and a public external standard to align to. The outcomes here follow the congruence strand of the New York State Next Generation Mathematics Learning Standards, so a learner’s progress maps directly onto what a New York school or Regents examination expects.

The current chain runs from precise definitions, through transformations and rigid motions, to congruence proofs, and reaches for the triangle congruence criteria, which exist as a stub waiting to be written.

Coherence map

Outcomes in this domain, layered by prerequisite. Begin with the first row.

Start here

Define the basic objects of plane geometryfoundation

After: Represent transformations in the plane

Step 2

Represent transformations in the planefoundation

Before: Define the basic objects of plane geometry

After: Describe and draw rotations, reflections, and translations

Step 3

Describe and draw rotations, reflections, and translationsintermediate

Before: Represent transformations in the plane

After: Use rigid motions to decide and prove congruence

Step 4

Use rigid motions to decide and prove congruenceadvanced

Before: Describe and draw rotations, reflections, and translations

After: Prove triangles congruent with SSS, SAS, and ASA

Step 5

Prove triangles congruent with SSS, SAS, and ASAadvancedstub

Before: Use rigid motions to decide and prove congruence

Courses

draft

Congruence Through Rigid Motions

Go from precise geometric definitions to proving triangles congruent with rigid motions, using only free resources.

• 4 outcomes
• ~12 hours

Credentials

draft

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.

• 4 outcomes