Right angles and parallel lines

A corner of paper is a measuring tool

Look at the corner of a notebook. Two edges meet in it “exactly straight” — not slanted out, not slanted in. Such a corner is called a right angle.

A right angle is the most important angle in the world: doors, windows, books, screens, tiles have it. A rectangle and a square, which you know from perimeter and area, have right angles in all four corners — that is exactly what makes them a rectangle and a square.

And here is the second idea of today: parallel lines. Those are two lines that go in the same direction all the time and never meet — like railway tracks. Opposite sides of a rectangle are parallel.

To spot a right angle you need no device: a corner of paper is an exact measuring tool that you always have to hand. Today you will learn to use it — and also to draw a right angle.

Ema helps dad hang a shelf and dad grumbles that it is crooked. “How do you know without a spirit level?” Ema asks. Dad takes a notebook from the table and puts the corner between the cupboard wall and the shelf: between the notebook edge and the shelf a gap yawns. “See? The notebook corner is a right angle. When the shelf does not line up with the corner, it is slanted.” He loosens the screw, lines it up, the gap disappears. Ema remembers the trick: a piece of paper is a measuring tool — only it must not be crumpled paper.

How to check, draw and find parallel lines

Right-angle test with a corner of paper:

1. Take a sheet of paper with a straight, uncrumpled corner (a notebook, a card).
2. Put the paper corner into the corner you are testing — vertex on vertex.
3. Do both paper edges line up with the arms of the angle? It is right. Does a gap show, or does an arm hide under the paper? It is not right.

An angle smaller than a right one (pointy like a beak) is called acute, a bigger one (opened) obtuse. It is enough that you can tell them from a right one.

Drawing a right angle: use a set square with a mark (a triangle ruler that has a right angle marked at one corner).

1. Draw the first line.
2. Put the mark (the square mark) on the line.
3. Draw the second line along the edge of the set square.

Two lines that make a right angle are called perpendicular.

You know parallel lines like this: they have the same distance between them everywhere. Measure the perpendicular distance between the lines in two different places — when it comes out the same, they are parallel. Railway tracks must have the same gauge everywhere, otherwise the train derails.

Checking the corners of a notebook

Task: check whether your notebook has right angles.

Step 1: I take a card with a sharp straight corner.

Step 2: I put it into the first corner of the notebook: vertex on vertex, edge on edge.

Step 3: does it line up? Yes — a right angle. One by one I check all four corners.

A notebook is a rectangle, so they all pass. If one did not line up, the notebook would be skewed — and even an eye would see that: the pages would not stack into a pile.

Drawing a perpendicular

Task: draw a perpendicular to a line.

Step 1: I draw line p along a ruler.

Step 2: I take a set square with a mark and put the mark exactly on line p.

Step 3: along the upright edge of the set square I draw a line. Done — a perpendicular.

Step 4: check with a corner of paper: I put the corner into the crossing. It lines up → the angle is right.

In the corner I draw a little curve with a dot — the mark that it really is a right angle.

Finding parallel lines

Task: are the lines in your notebook parallel?

Step 1: I pick two lines.

Step 2: I measure the distance between them at the left edge of the page: say 8 mm.

Step 3: I measure at the right edge: 8 mm again.

Conclusion: the same distance everywhere → parallel. That is why you write straight in a notebook — the lines lead the writing like tracks lead a train.

A counter-example: two lines that get closer to each other will meet somewhere — they are not parallel.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. 시작 with ten. When it goes well, add more.

Is that corner right? Compare it with a notebook corner in your head.

Practise the questions

On paper

Today you draw. A sharpened pencil, a ruler, a set square with a mark.

1. Walk the room and find five right angles (corners of doors, windows, books…). At each one check with a corner of paper and write where it was.

2. Draw a line and a perpendicular to it with a set square with a mark. Mark the right angle with a little curve with a dot.

3. Draw two parallel lines 3 cm apart. (Hint: in two places on a line mark 3 cm perpendicularly and join the points.)

4. Draw freehand three angles: acute, right and obtuse. Label them and check the right one with a corner of paper.

Now you 💪

1. You can check a right angle with a corner of paper: vertex on vertex, edges line up.
2. You draw a perpendicular with a set square with a mark.
3. You can explain parallel lines through railway tracks and the same distance everywhere.

What to take from this lesson

• A right angle is a corner “exactly straight” — like a notebook corner. It is marked with a little curve with a dot.
• Test: put a corner of paper. It lines up = right. A gap = it is not right.
• Perpendiculars are lines that make a right angle; they are drawn with a set square with a mark.
• Parallel lines go in the same direction and have the same distance everywhere — like railway tracks.
• A rectangle and a square: all right angles, opposite sides parallel.

© 2026 Ing. Martin Polak / AlgoRhino · 콘텐츠 이용 약관