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Constructing a trapezium

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

You learn the trapezium (das Trapez) and construct it with height, parallel line and two angles.
📄 Open worksheet (PDF, German)

The video

In the video the parallel is drawn with the set square turned round: a line parallel to the drawing edge lies on \(a\).

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

Contents of the video

  1. 0:00 Introduction
  2. 0:13 The trapezium
  3. 0:30 The sketch
  4. 0:47 Side, height, parallel
  5. 1:18 The angles
  6. 1:42 The description
  7. 2:09 Careful, mistake!
  8. 2:30 Try it yourself

The most important points

Properties

Two opposite sides are parallel: \(a \parallel c\). Their distance is the height (die Höhe) \(h\).

a \parallel c, the distance is the height h.
\(a \parallel c\), the distance is the height \(h\).

How to construct

1. Draw \(a\). 2. Height \(h\) as a perpendicular, then the parallel to \(a\). 3. \(\alpha\) at \(A\): \(D\). 4. \(\beta\) at \(B\): \(C\).

The finished trapezium: a = 6 cm, h = 3 cm, \alpha = 70^\circ, \beta = 60^\circ.
The finished trapezium: \(a = 6\) cm, \(h = 3\) cm, \(\alpha = 70^\circ\), \(\beta = 60^\circ\).
Mistake: the top line is drawn by eye and is not parallel.
Mistake: the top line is drawn by eye and is 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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Show the worksheet solutions
The worksheet – Page 4
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Try it yourself

Task

Is every parallelogram also a trapezium?

Show solution

Yes: it even has two pairs of parallel sides.

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: Trapez (a parallel zu c, Höhe h, Konstruktion mit Parallele und zwei Winkeln). 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.