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Drawing parallels

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

Two lines are parallel if they have the same distance everywhere. You draw parallels with the set square. The parallels to the drawing edge help you.
📄 Open worksheet (PDF, German)

The video

In the video the set square draws parallels: through a point, at a distance of 2 cm and to a slanted line.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:11 What is parallel?
  3. 0:33 Parallel through a point
  4. 1:25 Parallel at a distance
  5. 1:53 A slanted line
  6. 2:13 Careful, mistake!
  7. 2:34 Try it yourself

The most important points

Two lines are parallel if they have the same distance (der Abstand) everywhere. They never cross, like the rails of a train. We write \(g \parallel h\): “\(g\) is parallel to \(h\)”.

On the left and on the right the distance is 3 cm.
On the left and on the right the distance is 3 cm.

The parallel to \(g\) through \(P\)

Put a parallel to the drawing edge (die Parallele zur Zeichenkante) of the set square exactly on \(g\). The drawing edge goes through \(P\). Draw along the drawing edge. The parallels to the drawing edge are always 5 mm apart.

Distance 2 cm: the fourth parallel to the drawing edge lies on g (4 · 5 \text{ mm} = 2 \text{ cm}).
Distance 2 cm: the fourth parallel to the drawing edge lies on \(g\) (\(4 \cdot 5 \text{ mm} = 2 \text{ cm}\)).

Don't draw by eye! Always check the distance in two places.

2 cm on the left, 2.5 cm on the right: these lines are not parallel.
2 cm on the left, 2.5 cm on the right: these lines are not parallel.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
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The worksheet – Page 4
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The worksheet – Page 5
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Show the worksheet solutions
The worksheet – Page 6
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Try it yourself

Task

Which parallel to the drawing edge lies on \(g\)? a) distance 1 cm b) distance 3 cm c) distance 1.5 cm

Show solution

a) the 2nd parallel b) the 6th parallel c) the 3rd parallel (each parallel 5 mm)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: parallel lines, distance, drawing parallels with the parallels to the drawing edge of the set square. Ask me five short questions, one after the other. Always wait for my answer. Then tell me if it is right and explain briefly why. Use simple German sentences.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.