Congruence Through Rigid Motions
Go from precise geometric definitions to proving triangles congruent with rigid motions, using only free resources.
Define the basic objects of plane geometry
I can give precise definitions of angle, circle, perpendicular lines, parallel lines, and line segment, using the undefined notions of point, line, distance along a line, and distance around a circular arc.
- Domain
- Geometry
- Level
- foundation
- Status
- draft · v0.1.0
- License
- CC BY-SA 4.0
The vocabulary every later geometry outcome depends on. Precision matters here, because the proofs later in the chain rest on these definitions.
Learn first
Nothing. This is a starting point.
Learn it
Scope
Angle, circle, perpendicular lines, parallel lines, and line segment, each defined in terms of point, line, distance along a line, and distance around a circular arc.
Common misconceptions
- Treating “perpendicular” as “looks like a corner” rather than as lines meeting at a right angle.
- Defining a circle by its shape instead of as the set of points at a fixed distance from a center.
Resources
| Resource | Kind | Cost | Provider |
|---|---|---|---|
| Khan Academy, High School Geometry | video | free | Khan Academy |
Courses that include it
Prove it
Evidence of mastery
- Writes a definition of each term that a peer can use to decide whether a given figure is an example.
- Sorts a set of figures into examples and non-examples of each term and justifies each choice.
Assessments that measure it
No assessment yet.
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
- Represent transformations in the plane foundation unlocks 3 more