Lines, rays, line segments and how lines sit relative to… — 11–13
Tell a line from a ray and a segment, and name two lines as parallel, intersecting, perpendicular or oblique.
Line, ray, segment: who has a beginning and an end?
A line has no beginning and no end: it goes on for ever in both directions, so you can never draw all of it. A ray has one starting point, its origin, and goes on for ever in one direction. A line segment has two endpoints, so it has a length you can measure with a ruler. Through two different points there is exactly one line. Two lines in a plane are either parallel (they never meet) or intersecting (they meet at one point). If they meet at a right angle they are perpendicular, otherwise oblique.
Why we draw a piece and talk about the whole line
A sheet of paper is small and a line is endless, so what you draw is only a piece. The question that matters is: what would happen if you extended it? Two lines are parallel if, however far you extend them, they never meet: the distance between them stays the same, like the rails of a railway. Two intersecting lines would meet if you extended them, even when the drawing does not show it. And being perpendicular matters so much that it has its own tool: the set square.
Points, segment, ray and lines with a set square
Mark A and B 5 cm apart: the segment [AB] is 5 cm long. The line AB goes through A and B and on both sides. The ray from A through B starts at A and never stops: mark C on it with AC = 8 cm. Since 8 > 5, B lies between A and C, so BC = 8 − 5 = 3 cm. A point D on line AB, 2 cm from A on the other side, is not on the ray, and DC = 2 + 8 = 10 cm. With a set square, the lines through A and through C perpendicular to AB are parallel, 8 cm apart everywhere.
The trap: trusting only what is drawn
Two lines that do not touch on the page are not necessarily parallel: they may cross a bit further on, and then they are intersecting. To be more confident, measure the distance between them in several places: if it is always the same, they are parallel. Another mix-up: thinking perpendicular lines must be horizontal and vertical. Two lines that form a right angle are perpendicular even when tilted on the page: turn the page and see. And oblique lines are intersecting lines that do not form a right angle.
Where you see this outside school
The rails of a railway are parallel, the corner of a room joins edges that are perpendicular, and two roads that cross in an X are oblique lines. The beam of a torch is a good picture of a ray: it starts at the torch and goes straight on. The edge of a ruler draws line segments, which you can measure. On a map or a floor plan, streets that are parallel and perpendicular help you find your way.
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