A map that is right

Liri had drawn her star map freehand – the lines were crooked, the angles inaccurate.

Liri: “My map looks chaotic. The lines don’t fit together!”
Erklärus: “Then you need a Geodreieck – a set square with a protractor built in. With it you draw lines that are really straight – and angles that are really right.”

📐 What is a Geodreieck?

A Geodreieck is a transparent plastic triangle – a set square with a protractor – that combines three tools in one: a ruler, a protractor and a corner for right angles.

A real set square with labels
1
2
3
4
1Ruler – the long edge with cm and mm marks
2Degree scale – the yellow arc with numbers from 0° to 180°, the protractor
3Centre point – the little dot in the middle of the long edge, where you place the corner of an angle
4The 90° corner – this is where the two equally long edges meet at a right angle

🧭 Measuring and drawing an angle

The size of an angle is given in degrees (°). Here is what to do:

1️⃣ Place the centre point of the set square exactly on the corner of the angle (the vertex).
2️⃣ Line up the 0° line with one arm of the angle.
3️⃣ Where the other arm crosses the degree scale, read off the number of degrees.

Erklärus: “Important: always read from the scale that starts at the arm you lined up against – otherwise you accidentally read from the wrong side.”
Measuring an angle with a real set square
This is what measuring an angle with a real set square looks like – the 0° line lies along the first arm, and the second arm crosses the degree scale.
The angle in the picture is

✋ Holding the set square properly

One hand presses the set square firmly onto the paper without letting it slip. The other hand moves the pencil closely along the edge.

Erklärus: “The most common mistake: the set square slips while you draw. So really press it down firmly – even if that feels unusual at first.”

📏 Perpendicular lines

Two lines that meet at a right angle (90°) are called perpendicular to each other. For that you simply place the right-angled corner of the set square against them – the two short edges automatically show you 90°.

You mark a right angle like this: a small arc with a dot inside. With two perpendicular lines, all four angles are the same size – exactly 90°.

Perpendicular lines with a real set square
Two perpendicular lines: one runs along the edge of the set square, the other along its centre line – they meet at a right angle (90°).
Two lines meet at a 90° angle → perpendicular
Two lines meet at a 90° angle → parallel

📐 Drawing a parallel line – with the guide lines in the set square

Two lines that never meet and stay the same distance apart everywhere are called parallel. Inside the set square, several parallel guide lines are drawn – you use those:

1️⃣ Place the set square so that one of the guide lines lies exactly on your existing line.
2️⃣ Choose another guide line at the distance you want.
3️⃣ Draw along this second guide line with your pencil – and your parallel line is done!

Erklärus: “Because all the guide lines in the set square are already drawn parallel to each other, nothing can go wrong when you draw.”
Drawing a parallel line with the set square
The guide lines inside the set square are all drawn parallel to each other – simply choose the right one.

🔍 Recognising right angles

With the set square you can check whether a corner really is 90° – simply place the right-angled edge against it.

90° arc with a dot
A right angle measures exactly 90°. You recognise it by the little arc with a dot – and you check it with the right-angled corner of your set square.
A table corner – usually a right angle
The tip of a triangular ruler
🌌 Angles in the universe

Satellite solar panels are often aligned at a right angle to the Sun to collect as much energy as possible.
The orbits of some moons run almost parallel to the orbit of their planet.
Precise angle measurement is crucial for a rocket to reach exactly the right orbit – even a small error adds up over millions of kilometres.

❌ Common mistake

Many people only hold the set square loosely – then it slips while drawing, and the line comes out crooked.

Tip: really press down firmly, and keep the pencil close to the edge instead of holding it at an angle from above!

📐 Exercise 1
Two lines that never meet and always stay the same distance apart are called…
perpendicular
parallel
📏 Exercise 2
How many degrees is a right angle?
🔍 Exercise 3
How do you hold the set square in place when drawing?
With one hand, pressed down firmly
Not at all, it stays still by itself

A map you can trust

Liri drew her star map again – this time with straight lines and real right angles.

Liri: “Now my map looks like a proper map.”
Erklärus: “And that is exactly why you can trust it now. A crooked line can send you in the wrong direction – an accurate one can’t.”
“Set square: press down firmly, guide the pencil close to the edge. Perpendicular = 90° angle. Parallel = never meeting, always the same distance apart.”
What you learned today
Perpendicular = 90°  ·  Parallel = never meeting
Press the set square down firmly, guide the pencil close to the edge
🌟

Chapter 18 mastered!

Liri can now draw precisely – straight lines, right angles and parallels.

Erklärus’s notebook – page 18:
“Set square: press down firmly, pencil close to the edge. Perpendicular lines meet at a right angle (90°). Parallel lines never meet and always stay the same distance apart.”
← Back to overview 18 – Set Square