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Rotational and point 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 rotational symmetry and point symmetry mean, and you find the angle of rotation.
📄 Open worksheet (PDF, German)

The video

In the video a pink copy of the figure turns around the centre of rotation. If it fits, the figure has rotational symmetry.

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 Rotational symmetry
  3. 0:23 The angle of rotation
  4. 1:00 Point symmetry
  5. 1:32 Careful, mistake!
  6. 1:50 Try it yourself

The most important points

Rotational symmetry

You turn a figure around a centre of rotation (der Drehpunkt) \(D\). Afterwards it looks the same: it has rotational symmetry (drehsymmetrisch). The number of degrees is the angle of rotation (der Drehwinkel).

An equilateral triangle fits after 120^\circ.
An equilateral triangle fits after \(120^\circ\).

Point symmetry

A half turn (\(180^\circ\)) around the centre of symmetry (der Symmetriepunkt) \(S\), and the figure looks the same: it has point symmetry (punktsymmetrisch). Every figure with point symmetry also has rotational symmetry.

The parallelogram has point symmetry, S is the middle.
The parallelogram has point symmetry, \(S\) is the middle.

The equilateral triangle has rotational symmetry, but no point symmetry.

After 180^\circ the triangle is upside down: it does not fit.
After \(180^\circ\) the triangle is upside down: it does not fit.

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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Show the worksheet solutions
The worksheet – Page 5
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Try it yourself

Task

Smallest angle of rotation? a) square b) equilateral triangle c) rectangle. d) Which of them have point symmetry?

Show solution

a) \(90^\circ\) b) \(120^\circ\) c) \(180^\circ\) d) square and rectangle

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: rotational and point symmetry (Drehpunkt, Drehwinkel, Symmetriepunkt, halbe Drehung). 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.