GEO / Introduction
Introduction to Geometry
Shape Harbor
Reason about angles, shape, similarity, measurement and coordinates.
Preparation: Fractions, ratios, basic equations and square roots.
Current coverage: 12 core stages: angle reasoning, congruence, similarity, circles, coordinates and solids.
LEVEL 1 · DIFFICULTY 1/5 within this course
Angles and Congruence
Use relationships to justify missing measures.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 108 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 2 · DIFFICULTY 2/5 within this course
Similarity and Right Triangles
Connect scale, area and distance.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 108 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 3 · DIFFICULTY 3/5 within this course
Polygons and Circles
Reason about turns, arcs and intersecting chords.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 108 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 4 · DIFFICULTY 4/5 within this course
Coordinates and Solids
Move between diagrams, coordinates and measurement.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 108 checked variations · 2 × 6 assessment questions
Read the lessons →Progress earned through practice
Earn two independent practice stars and one application star, then complete the library skill check for that stage. The check covers the stage’s library prompts, so changing numbers alone is not enough. Hints help you learn; your existing stars and earned rewards stay yours. Clear every stage to clear a level.
Every stage includes an explanation, two worked examples and eight library practice problems, plus checked variations with changing numbers and applications. Each level also has a separate unit test and a later review form. Parents see actual attempts, hint use and results.
These are independently authored core-skills courses, with the current scope listed for each course. They do not reproduce complete textbook contents. Difficulty describes the teaching sequence within each course; course preparation matters when comparing subjects. This site is not affiliated with or endorsed by AoPS. Results reflect these exercises and are not standardized scores. Content release math-courses-2026.09.27-university-guides-v2.