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Line symmetry

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

You learn what symmetrical about an axis means, find axes of symmetry and reflect points and figures with the set square.
📄 Open worksheet (PDF, German)

The video

In the video we fold: one half flips onto the other. The axis of symmetry is dashed in pink.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:18 Symmetrical about an axis
  3. 0:42 Finding axes of symmetry
  4. 1:08 Reflecting a point
  5. 1:52 Reflecting a figure
  6. 2:11 Careful, mistake!
  7. 2:32 Try it yourself

The most important points

Line symmetry

A line \(g\) divides a figure into two equal halves. Then the figure is symmetrical about an axis (achsensymmetrisch). \(g\) is the axis of symmetry (die Symmetrieachse) or mirror axis (die Spiegelachse). Rectangle: 2 axes, square: 4.

Rectangle with 2 and square with 4 axes of symmetry.
Rectangle with 2 and square with 4 axes of symmetry.

Reflecting a point

Zero line on \(g\), drawing edge through \(P\). Read the distance from \(P\) to \(g\). Go the same distance on the other side: that is \(P'\) (P prime, P Strich). \(\overline{PP'}\) is perpendicular to \(g\).

P and P' are the same distance from g: 3 cm each.
\(P\) and \(P'\) are the same distance from \(g\): 3 cm each.

The diagonal of a rectangle is not an axis of symmetry: if you fold on it, the halves do not fit.

Mistake: folding on the diagonal, the halves do not fit onto each other.
Mistake: folding on the diagonal, the halves do not fit onto each other.

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

How many axes of symmetry? a) square b) rectangle c) equilateral triangle d) parallelogram

Show solution

a) 4 b) 2 c) 3 d) 0

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: line symmetry (achsensymmetrisch, Symmetrieachse, Spiegelachse, Punkte mit dem Geodreieck spiegeln). Give me five short tasks, 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.