Back to the path
⊥

Perpendicular lines, parallel lines and the right angle

Level 2 · Ages 8–11

Quick recall· Let's wake up what you already know before we start.

Review: which of these three geometric objects goes on forever in both directions?

The whole lesson

Read it again any time, including while you work through the exercises.

Look at the corner of a sheet of paper, the crossing lines of floor tiles, the angle of a window: right angles are everywhere. A right angle is the perfect corner, the one that leans neither one way nor the other. To check it, geometers use a magic tool: the set square. If the corner of the set square fits exactly into the angle, it is a right angle.

When two lines cross and form a right angle, we say they are perpendicular. Think of a plus sign (+) or a street crossing another one squarely: four right angles appear around the crossing. We write this relation with the symbol ⊥, which itself looks like two perpendicular segments.

Now picture two train rails on flat ground: they run side by side, always the same distance apart, and never cross. These are parallel lines. Even if you extend them very far, they will never touch. The gap between them stays constant, like the two edges of a ruler.

Watch out for the trap: two lines that cross are not always perpendicular! You really need a right angle, checked with the set square. Two lines that cross at a slant are just intersecting. In this lesson, you will learn to spot these situations at a glance, then check them like a true geometer, with a set square and a ruler.

The worked example, step by step

Lines (a) and (b) cross each other. How do you check whether they are perpendicular?

  1. Équerre sur (a)

    I place one side of my set square's right angle along line (a), with the corner of the set square right on the crossing point.

  2. Autre côté sur (b) ?

    I look at the other side of the set square's right angle: does it follow line (b) exactly, with no overlap and no gap?

  3. Oui : (a) ⊥ (b)

    It follows (b) perfectly: the angle is right, so the lines are perpendicular. I write (a) ⊥ (b) and mark the angle with a small square.

Result: Lines (a) and (b) are perpendicular: (a) ⊥ (b).