The point

Geometry is built from three plain ideas, and the simplest is the point. A point marks an exact position — a single spot — and nothing more. It has no size at all: no width, no height, no thickness. The dot we draw is only a marker; the true point is the precise place at its centre.

We name a point with a single capital letter, so we can talk about it: point A, point B, and so on.

Lines, segments and rays

A line is perfectly straight and goes on forever in both directions — it never bends and never stops. We draw little arrowheads on each end to remind us that it keeps going past the edge of the page.

Two related shapes are just parts of a line:

• a line segment is the piece between two points — it has two ends, like the segment from A to B;
• a ray starts at one point and goes on forever in one direction — one end, like a beam of light from a torch.

There is one more quietly important fact: through any two distinct points there passes exactly one straight line. Pick two spots and there is one — and only one — perfectly straight line that joins them.

The plane

A plane is a perfectly flat surface that extends forever in every direction — imagine a tabletop that never reaches an edge. Points and lines live in planes: a plane is the endless flat sheet on which we draw our geometry.

Points that all lie on one straight line have a special name — they are collinear. Step through the figure to watch a point grow into a line, a segment and a ray, and finally a whole plane.