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Curriculum & Standards · Geometry (Secondary)

Secondary Geometry, with formal proofs and the trigonometry the world expects.

Two-column / paragraph / flow proofs, congruence and similarity proven from first principles, sin / cos / tan + special right triangles + sine and cosine rules, eight circle theorems including the alternate segment theorem, the equation of a circle, surface area and volume of every standard 3D solid (including frustums), classical compass-and-straightedge constructions and locus. Calibrated to CCSS HS Geometry + Singapore Secondary 3-4 + Cambridge IGCSE 0580 Extended.

64

Skills

11

Modules (hex)

11

Official standards benchmarked

14–16

Age coverage

Why proofs and circle theorems are non-negotiable

TIMSS 2023 Grade 8 ranks Singapore at the top. CCSS HS Geometry is the only mainstream standard that requires deriving congruence criteria from rigid motions and proving the Pythagorean theorem; Singapore Sec 3-4 and Cambridge IGCSE Extended both demand the eight circle theorems and trigonometry of oblique triangles via the sine and cosine rules. Rodybee tracks the union of these expectations.

#CountryTIMSS score
1🇸🇬Singapur605
2🇹🇼Chinese Taipei597
3🇰🇷Corea596
4🇯🇵Japón595

Source: TIMSS 2023 Grade 8 Math Achievement ↗

Find your child's level

Pick an age and see exactly what we teach at that point — and what the most demanding standards in the world expect at the same age. There's no marketing fluff: each topic links to the official curriculum document.

Your child's age

Rodybee for your child · 7 años

What we teach at this age

No skills calibrated for this exact age yet — try an adjacent year.

Highest international bar at this age · G9 / Sec 3 / Y10

🇺🇸Estados Unidos

Razonamiento formal (two-column / paragraph / flow proof), líneas y ángulos con teoremas, congruencia formal (SSS, SAS, ASA, AAS, HL), triángulos y cuadriláteros con propiedades demostradas, similitud completa con criterios AA/SAS/SSS y factor de escala k/k²/k³.

Grade-by-grade benchmark

Full table of what each major standard expects per grade. Every cell is sourced from the official ministry, board or framework document.

G9 / Sec 3 / Y10

First half — proofs + congruence + similarity (~14–15 años)

Highest bar · 🇺🇸 Estados Unidos

Razonamiento formal (two-column / paragraph / flow proof), líneas y ángulos con teoremas, congruencia formal (SSS, SAS, ASA, AAS, HL), triángulos y cuadriláteros con propiedades demostradas, similitud completa con criterios AA/SAS/SSS y factor de escala k/k²/k³.

CountryExpected topicsOfficial source
🇺🇸Estados UnidosG-CO (Congruence): definir vía rigid motions, derivar SSS/SAS/ASA, demostrar theorems clásicos. G-SRT (Similarity): definir vía dilatación, AA/SAS/SSS de similitud. Two-column proof formal.CCSS-M HS Geometry ↗
🇸🇬SingapurSec 3 Express: congruence y similarity con applications, propiedades de cuadriláteros, geometric reasoning.Singapore MOE Lower Secondary Mathematics Syllabus (Express) ↗
🇬🇧Reino UnidoGCSE Higher: criterios formales de congruencia, similarity con scale factor incluido k² y k³, proofs informales.UK GCSE Mathematics Subject Content ↗
🇦🇺AustraliaYear 9-10A: congruence y similarity con razonamiento deductivo. Geometric proofs introducidas.ACARA Australian Curriculum Mathematics Year 9-10 v9.0 ↗

Rodybee skills at this grade

Formal geometry notation · Conditional statements · Inductive vs deductive reasoning · Two-column proof · Paragraph proof · Flow proof · Prove: vertical angles theorem · Prove: parallels & transversal · Prove: perpendicular bisector · Prove: triangle sum 180° · Exterior angle theorem · Congruence — rigid motion definition · Congruence — SSS · Congruence — SAS · Congruence — ASA / AAS · Congruence — HL (right triangle) · Apply congruence in a proof · Isoceles base angles · Midsegment theorem · Parallelogram properties (proof) · Rectangle / rhombus / square (proof) · Trapezoid properties · Similarity — dilation definition · Similarity — AA · Similarity — SAS / SSS · Triangle proportionality · Scale factor (k, k², k³) · Apply similarity in a proof

G10 / Sec 4 / Y11

Second half — trigonometry + circles + analytic + 3D + constructions (~15–16 años)

Highest bar · 🇸🇬 Singapur

Trigonometría del triángulo rectángulo y oblicuo (ley de senos y cosenos), círculos avanzado (8 theorems), geometría analítica (ecuación del círculo, distance, midpoint, line-circle intersection), 3D avanzado (surface area, volumen frustum, cross-sections, Cavalieri), constructions formales con compás/regla, modeling con density y optimization.

CountryExpected topicsOfficial source
🇸🇬SingapurSec 3-4 Express: 8 circle theorems explícitos (incl. alternate segment), trig 3D incluido ángulo línea-plano, sine/cosine rules como herramientas universales, frustums y mensuration completa.Singapore MOE Lower Secondary Mathematics Syllabus (Express) ↗
🌐Cambridge IGCSE 0580 ExtendedGeometry & Trigonometry completa: 8 circle theorems, sine/cosine rules, surface area y volumen completo (incluido frustum), constructions formales.Cambridge IGCSE Mathematics 0580 ↗
🇺🇸Estados UnidosG-SRT (Trig + Pythagoras), G-C (Circle theorems), G-GPE (Coordinate geometry, equation of circle), G-GMD (Volume + Cavalieri), G-MG (Modeling). Sine/cosine rules son (+) opcional.CCSS-M HS Geometry ↗
🇬🇧Reino UnidoGCSE Higher Y10-Y11: circle theorems, trig en triángulos no rectángulos, vectores básicos, ecuación del círculo.UK GCSE Mathematics Subject Content ↗
🇦🇺AustraliaYear 10A: trig completa con sine/cosine rules, circle theorems, ecuación del círculo, surface area 3D.ACARA Australian Curriculum Mathematics Year 9-10 v9.0 ↗

Rodybee skills at this grade

Trig ratios (sin / cos / tan) · Special right — 30°-60°-90° · Special right — 45°-45°-90° · Solve a right triangle · sin θ = cos(90° − θ) · Elevation & depression angles · Law of sines · Law of cosines · Triangle area = ½ ab sin C · Solve oblique triangles · Inscribed angle theorem · Tangent ⊥ radius · Two tangents from external point · Alternate segment theorem · Arc length & sector area · Segment area · Distance formula (apply) · Midpoint formula · Circle equation · Circle from completing the square · Line-circle intersection · Coordinate proof · 3D surface area · Volume of a frustum · Cross-sections of solids · Cavalieri's principle · Construction — bisect segment · Construction — bisect angle · Construction — perpendicular · Construction — parallel · Construction — equilateral · Locus · Density (area & volume) · Geometric design problem · Geometric optimization · 3D trigonometry

Full research document

Methodology, gap analysis, recommendations and the complete list of sources are in the underlying research markdown.

Read the full benchmark document →
Geometry (Secondary) Curriculum & Standards — Rodybee