Geometry

Geometry is the language of shape and space, from the lines that define a building to the hidden patterns in a circle.

The Map of Space

You have explored shapes on coordinate grids using equations. Now let us study the shapes themselves — their angles, properties, and constructions.

Geometry is like the blueprints for the physical world. We start with the basic vocabulary of lines and shapes, then learn to build them precisely with tools. We'll explore how objects shrink and grow through similarity, and finally, we'll unlock the ancient secrets of angles and circles. Ready to see the math behind the world's design?

Key idea

Ready to see the math behind the world's design?

Memory trick

Think of geometry as 'Earth Measurement' — the math that builds our reality.

What You Will Learn

You will learn the vocabulary first, then the angle rules, then the rules for scaling shapes up and down, and finish with the circle theorems that carry the hardest marks on the paper.

Steps

1
Classifying angles, triangles, quadrilaterals and polygons, and their properties.
2
Angle rules: at a point, on a line, in parallel lines, and inside polygons.
3
Congruence and similarity, including area and volume scale factors.
4
Symmetry in two and three dimensions, constructions and scale drawings.
5
Circle theorems: semicircle, centre, same segment, cyclic quadrilateral, alternate segment.
6
Combining several theorems to reason through a multi-step angle chase.

Formula

The one that unlocks polygons:

sum of interior angles = (n - 2) \times 18 0^{\circ}

And the exterior angles of any polygon always sum to $36 0^{\circ}$ .

Practise geometry now

Interactive visual aids, then real past-paper questions marked on your working like the exam. Free to start.

Practise free on Lemmara

Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education or Pearson Edexcel. The lessons and worked examples are Lemmara’s own.