Standard syllabus
Geometry · Undergraduate · Math
Learning objectives from the Geometry syllabus, grouped by unit. Click an objective for study materials.
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Geometry — scope drawn from open college geometry texts and typical US Euclidean / transformational geometry syllabi.
Euclidean foundations
- Axiomatic systems — Axiomatic systems; points, lines, and planes
- Angles and parallel lines — Angles and parallel lines
- Triangle congruence (SAS, ASA, SSS) — Triangle congruence (SAS, ASA, SSS)
- Similarity and proportional segments — Similarity and proportional segments
- Right triangles — Right triangles
- Special triangles — Special triangles
- Circles: chords, tangents, inscribed angles, and arc measure — Circles: chords, tangents, inscribed angles, and arc measure
Coordinate and solid geometry
- Coordinate geometry: distance, midpoint, and slope — Coordinate geometry: distance, midpoint, and slope
- Equations of lines — Equations of lines
- Circles in the plane — Circles in the plane
- Area and perimeter formulas — Area and perimeter formulas; surface area and volume of solids
- Cross-sections and nets of 3D figures — Cross-sections and nets of 3D figures
- Basic geometric constructions with compass — Basic geometric constructions with compass
- Straightedge — Straightedge
Transformations and symmetry
- Translations, rotations, and reflections — Translations, rotations, and reflections
- Glide reflections — Glide reflections
- Congruence — Congruence
- Similarity via transformations — Similarity via transformations
- Symmetry groups of regular figures (informal) — Symmetry groups of regular figures (informal)
- Tessellations and patterns in the plane — Tessellations and patterns in the plane
- Introduction to non-Euclidean geometry (overview) — Introduction to non-Euclidean geometry (overview)
Learning objectives
Click an objective for study materials.
Euclidean foundations
- Axiomatic systems — Axiomatic systems; points, lines, and planes
- Angles and parallel lines — Angles and parallel lines
- Triangle congruence (SAS, ASA, SSS) — Triangle congruence (SAS, ASA, SSS)
- Similarity and proportional segments — Similarity and proportional segments
- Right triangles — Right triangles
- Special triangles — Special triangles
- Circles: chords, tangents, inscribed angles, and arc measure — Circles: chords, tangents, inscribed angles, and arc measure
Coordinate and solid geometry
- Coordinate geometry: distance, midpoint, and slope — Coordinate geometry: distance, midpoint, and slope
- Equations of lines — Equations of lines
- Circles in the plane — Circles in the plane
- Area and perimeter formulas — Area and perimeter formulas; surface area and volume of solids
- Cross-sections and nets of 3D figures — Cross-sections and nets of 3D figures
- Basic geometric constructions with compass — Basic geometric constructions with compass
- Straightedge — Straightedge
Transformations and symmetry
- Translations, rotations, and reflections — Translations, rotations, and reflections
- Glide reflections — Glide reflections
- Congruence — Congruence
- Similarity via transformations — Similarity via transformations
- Symmetry groups of regular figures (informal) — Symmetry groups of regular figures (informal)
- Tessellations and patterns in the plane — Tessellations and patterns in the plane
- Introduction to non-Euclidean geometry (overview) — Introduction to non-Euclidean geometry (overview)
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Euclidean foundations
Axiomatic systems; points, lines, and planes
Coming soon - Coordinate and solid geometry
Coordinate geometry: distance, midpoint, and slope
Coming soon - Transformations and symmetry
Translations, rotations, and reflections
Coming soon
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