Points, lines and rays

Geometry has a few building blocks. The first is a point. Mark a dot with a sharp pencil: the sharper the tip, the thinner the dot. A point is an exact location: it has no length, no breadth and no height. It only tells you where. The tip of a compass, the sharpened end of a pencil and the point of a needle are models of a point. We name a point with one capital letter: Point Z, Point P, Point T.

Fold a piece of paper and unfold it: the crease gives the idea of a line segment. Mark two points A and B. There are many routes from A to B, curvy and straight. The shortest one, including A and B, is the line segment AB (or BA). A and B are its two end points. A segment is like a piece cut from a long sari: it has two ends, and you can measure it.

Now imagine segment AB carried on beyond A and beyond B, without any end. That is a line. It goes on forever in both directions, so we can never draw all of it; even a line drawn with a thick pen is only a picture of one. The line through A and B is called line AB; sometimes a line is named by a small letter, like l or m. Through any two points there is exactly one line.

A ray starts at one point and goes on endlessly in one direction only, like the beam of a lighthouse, the light of a torch, or the Sun's rays. A ray that starts at A and passes through P is called ray AP: the starting point is always written first.

In your book, a ray starts at O and passes through A and then B. It can be named OA or OB: both start at O and go the same way. But it cannot be called AO: ray AO would start at A.