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Similar figures

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

Similar figures (ähnliche Figuren) have the same shape, but not necessarily the same size. All sides are enlarged or reduced by the same factor.
📄 Open worksheet (PDF, German)

The video

In the video we compare two enlargements of a photo, find the scale factor \(k\) and the centre of enlargement \(Z\).

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

Contents of the video

  1. 0:00 Introduction
  2. 0:16 Similar or not?
  3. 0:33 Finding the scale factor
  4. 1:00 Finding the centre
  5. 1:28 Careful, mistake!
  6. 1:49 Try it yourself

The most important points

Similar

Two figures are similar if all sides are stretched by the same factor \(k\). The angles stay the same.

Enlargement 1 is similar, enlargement 2 is distorted.
Enlargement 1 is similar, enlargement 2 is distorted.

Scale factor

\(k = \text{image length} : \text{original length}\). \(k > 1\): enlarge, \(k < 1\): reduce.

k = 5 : 2 = 2{,}5; check: 2{,}5 · 3\,\text{cm} = 7{,}5\,\text{cm}.
\(k = 5 : 2 = 2{,}5\); check: \(2{,}5 \cdot 3\,\text{cm} = 7{,}5\,\text{cm}\).

The lines through image point and original point meet in the centre of enlargement \(Z\) (Streckzentrum).

ZA' = 2 · ZA, so k = 2.
\(ZA' = 2 \cdot ZA\), so \(k = 2\).

Careful: do not calculate original : image! \(2 : 5 = 0{,}4\) would mean reducing.

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

A rectangle is \(4\,\text{cm}\) long and \(2{,}5\,\text{cm}\) wide. A similar rectangle is \(10\,\text{cm}\) long. What is \(k\)? How wide is it?

Show solution

\(k = 10 : 4 = 2{,}5\); width \(2{,}5 \cdot 2{,}5\,\text{cm} = 6{,}25\,\text{cm}\).

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: similar figures, scale factor and centre of enlargement (ähnliche Figuren). 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.