Subject

Geometry

Geometry is at the heart of our teaching philosophy. Spatial reasoning develops the visual intuition that makes every branch of mathematics more accessible. We teach geometry deeply — not as a collection of formulas, but as a system of logical relationships.

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The Geometry pathway

First Primary Junior Intermediate Senior

Ages 11–13 · Years 7–8

Euclidean reasoning and proof

Junior students begin writing geometric proofs and reasoning about congruence and similarity. This is where geometry transitions from visual intuition to rigorous logical argument — a transformative step in mathematical development.

What we cover

Congruence and similarity theorems
Angles in triangles and polygons
Parallel lines and transversals
Introduction to Euclidean proof
Pythagorean theorem and its applications

Competitions & exams we prepare for in United Kingdom

JMC
Kangaroo

Olympiad curriculum

Durable mathematical ideas form the curriculum; individual puzzles and practice lessons sit beneath them. Topics recur at increasing depth across the pathway.

Euclidean Proof

Definitions, Axioms and Theorems
Direct Proof and Chains of Deduction
Converse Statements and Counterexamples
Proof by Contradiction in Geometry
Collinearity and Concurrency
Choosing and Justifying Auxiliary Constructions

Triangles & Quadrilaterals

Triangle Congruence in Multi-Step Proofs
Similarity of Triangles
Ratios from Parallel Lines
Angle-Bisector Theorem
Medians, Altitudes and Perpendicular Bisectors
Midpoint and Midline Theorems
Pythagorean Theorem and Its Converse
Parallelogram and Trapezium Theorems
Kite and Rhombus Configurations
Homothety: Introduction

Circle Geometry

Chords, Arcs and Central Angles
Angles Subtended by the Same Chord
Cyclic Quadrilaterals
Tangent-Chord Theorem
Equal Tangents from a Point
Incircle and Circumcircle of a Triangle
Proving Four Points Are Concyclic
Power of a Point: Introduction

Olympiad Methods & Constructions

Area Methods and Equal-Area Arguments
Related lessonsDoubling the MedianOpens on Problems.cc
Double-Area and Area-Ratio Methods
Reflection and Shortest-Path Problems
Rotation by 60° and Equilateral Constructions
Geometric Loci
Straightedge-and-Compass Construction Problems
Geometric Invariants in Tiling and Dissection
Coordinates as a Checking Method

Inequalities & Extremal Geometry

Triangle and Polygon Inequalities
Broken-Line and Shortest-Path Problems
Extremal Points and Configurations
Geometric Covering and Packing Problems

Geometry

This course encompasses a range of Geometry topics such as coordinate and spatial geometry, introductory trigonometry, angles, parallel lines, congruent and similar triangles, polygons, circles, the Pythagorean Theorem, and more. Emphasis will be placed on reinforcing Algebra skills and enhancing critical thinking through problem-solving in both mathematical and real-world contexts.

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Articles

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Geometry3 min read

Diving Deep into Geometry: Exact Science's Camp Goes Beyond the Classroom

Why serious geometry still needs more proof, construction, and precision than most students ever get in school, and why that matters for mathematical maturity.

George Ionitsa·19 February 2024

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Geometry

Shapes, symmetry and visual puzzles

Shapes, symmetry and spatial intuition

Euclidean reasoning and proof

Circle theorems and classical constructions

Advanced Euclidean and projective geometry

Geometry

Diving Deep into Geometry: Exact Science's Camp Goes Beyond the Classroom

Start your Geometry journey