Course

Book 1. Foundations of Olympiad Geometry

Book 1. Foundations of Olympiad Geometry

  • 1. Angles, Lines and Parallel Lines
  • 2. Triangles I: Congruence
  • 3. Triangles II: Similarity
  • 4. Quadrilaterals
  • 5. Circles I: Basic Circle Geometry
  • 6. Areas I
  • 7. Basic Constructions and Auxiliary Lines
  • 8. Mixed Problems I
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Theory Examples Practice Ladders

Chapters

Chapters

Chapter

Angles, Lines and Parallel Lines

This module teaches students to work confidently with vertical and adjacent angles, parallel lines, the angle sum of a triangle, exterior angles, and the first angle-chasing problems.

20 Problems
Theory Examples Practice

Chapter

Triangles I: Congruence

This module teaches students to recognise congruent triangles, use SSS, SAS, and ASA, and work with isosceles triangles, medians, angle bisectors, and the first auxiliary constructions.
29 Problems
Theory Examples Practice

Chapter

Triangles II: Similarity

This module introduces triangle similarity, the AA, SAS, and SSS criteria, proportions, the midline of a triangle, and area ratios of similar figures.
21 Problems
Theory Examples Practice

Chapter

Quadrilaterals

This module teaches how to work with parallelograms, rectangles, rhombi, squares, trapezoids, the midline of a trapezoid, and first criteria for cyclic quadrilaterals.
24 Problems
Theory Examples Practice

Chapter

Circles I: Basic Circle Geometry

The main first-level circle module: central and inscribed angles, equal chords, tangents, the tangent-chord angle, and systematic work with cyclic quadrilaterals.
35 Problems
Theory Examples Practice

Chapter

Areas I

This module introduces triangle area as an olympiad tool: equal bases and heights, area ratios, medians, triangle partitions, and area chasing.
31 Problems
Theory Examples Practice

Chapter

Basic Constructions and Auxiliary Lines

A practical toolbox module on adding points, extending sides, drawing parallels and circles in order to find hidden congruent triangles, parallelograms, similarity, and cyclic quadrilaterals.
26 Problems
Theory Examples Practice

Chapter

Mixed Problems I

The final mixed module of Part I: the student does not know the method in advance and must choose between angles, congruence, similarity, circles, areas, and auxiliary constructions.
30 Problems
Theory Examples Practice