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Drawing perpendiculars

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

Two lines are perpendicular to each other if they make a right angle. You draw perpendiculars with the set square and learn about the foot and the distance.
📄 Open worksheet (PDF, German)

The video

In the video the set square draws perpendiculars: through a point on the line, through a point next to it 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. 0:14 What is perpendicular?
  3. 0:43 Point on the line
  4. 1:18 Point next to the line
  5. 1:52 The distance
  6. 2:03 A slanted line
  7. 2:22 Careful, mistake!
  8. 2:46 Try it yourself

The most important points

Two lines are perpendicular (senkrecht) to each other if they make a right angle (\(90^\circ\)). We write \(g \perp h\): “\(g\) is perpendicular to \(h\)”. Perpendicular does not always mean “from top to bottom”.

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

Put the zero line (die Nulllinie) of the set square exactly on \(g\). Slide the set square along \(g\) until the drawing edge goes through \(P\). Draw along the drawing edge.

The perpendicular h through P makes a right angle with g.
The perpendicular \(h\) through \(P\) makes a right angle with \(g\).

The perpendicular meets \(g\) at the foot (der Fußpunkt) \(F\). The length of the segment \(\overline{PF}\) is the distance (der Abstand) from \(P\) to \(g\): the shortest way.

The distance from P to g is 5 cm.
The distance from \(P\) to \(g\) is 5 cm.
Right: zero line on g. The short side makes only 45^\circ.
Right: zero line on \(g\). The short side makes only \(45^\circ\).

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
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Try it yourself

Task

Complete: a) A right angle is \(?^\circ\). b) When you draw, the ? of the set square lies on \(g\). c) The perpendicular meets \(g\) at the ?

Show solution

a) \(90^\circ\) b) zero line (die Nulllinie) c) foot (der Fußpunkt)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: perpendicular lines, right angle, drawing perpendiculars with the set square, foot and distance. 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.