Mathematics · Grade 10

Geometry

Proof, congruence, similarity, trigonometry and circles.

Taught byMarcus Ellery · Ivana Petrović

5units
20lessons
15–16typical age
Common Corestandards

Units

Unit 1: Foundations and proofStandards: G-CO.A.1, G-CO.C.9–11, G-CO.D.12 · 4 lessons
1. Points, lines, planes and definitions
2. Constructions with compass and straightedge
3. Angle relationships and parallel lines
4. Writing proofs
Unit 2: Transformations and congruenceStandards: G-CO.A.2–5, G-CO.B.6–8 · 4 lessons
1. Rigid motions
2. Symmetry
3. Triangle congruence criteria
4. Proving triangles congruent
Unit 3: Similarity and right-triangle trigonometryStandards: G-SRT.A.1–3, G-SRT.B.4–5, G-SRT.C.6–8 · 4 lessons
1. Dilations and similar figures
2. Proving triangles similar
3. Sine, cosine and tangent
4. Solving right triangles
Unit 4: CirclesStandards: G-C.A.1–3, G-C.B.5, G-GPE.A.1 · 4 lessons
1. Arcs, chords and inscribed angles
2. Tangents
3. Arc length and sector area
4. The equation of a circle
Unit 5: Coordinates, area and volumeStandards: G-GPE.B.4–7, G-GMD.A.1–3, G-MG.A.1–3 · 4 lessons
1. Proving properties with coordinates
2. Perimeter and area on the coordinate plane
3. Volume formulas and Cavalieri's principle
4. Modelling with geometry

Who teaches you

Every lesson has a named AI teacher and a mentor who keeps you on track. Both are AI, and every screen says so.

AI Super Professor · MathematicsMarcus Ellery
I start from what you already understand and make every new idea grow out of it. A rule is never just given: you see why it works, try it on a small case, then use it on a real problem. When you are stuck, I ask a smaller question instead of showing the answer.
- Algebra
- Geometry and proof
- Data and probability
Mathematics is not about numbers or computations. It is about understanding.
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AI Super Mentor · MathematicsIvana Petrović
I do not teach the lessons; Marcus does. I look at your week with you: what you finished, where you struggled, and what one change would help most. Then we write a short plan you can keep.
- Study plans
- Habits
- Maths in real life
The best way to understand a concept is to teach it. The second best is to apply it.
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How lessons run

Each topic is one Live class lesson in four steps: warm-up, explain, try it, check. The AI tutor gives hints, not answers, and waits for the learner to think.