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Kite and rhombus

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

You learn the properties of the kite (der Drachen) and the rhombus (die Raute) and construct a kite.
📄 Open worksheet (PDF, German)

The video

In the video the kite is constructed from its axis of symmetry \(\overline{BD}\) and two arcs.

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 The kite
  3. 0:57 The rhombus
  4. 1:13 The sketch
  5. 1:32 Constructing the kite
  6. 2:16 The description
  7. 2:38 Careful, mistake!
  8. 2:59 Try it yourself

The most important points

Properties

Kite: two pairs of adjacent sides of equal length, the diagonal \(\overline{BD}\) is the axis of symmetry, the diagonals are perpendicular. Rhombus: all four sides of equal length – a special kite.

Two pairs of adjacent sides are of equal length.
Two pairs of adjacent sides are of equal length.

How to construct

1. Draw \(\overline{BD}\) (axis of symmetry). 2. Arc around \(B\) with \(\overline{AB}\). 3. Arc around \(D\) with \(\overline{AD}\). 4. The intersections are \(A\) and \(C\).

The finished kite: \overline{BD} = 6 cm, \overline{AB} = 4.5 cm, \overline{AD} = 3 cm.
The finished kite: \(\overline{BD} = 6\) cm, \(\overline{AB} = 4.5\) cm, \(\overline{AD} = 3\) cm.
Mistake: 2.5 cm + 3 cm is shorter than 6 cm – the arcs do not meet.
Mistake: \(2.5\) cm \(+ 3\) cm is shorter than \(6\) cm – the arcs do not meet.

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
Page 1/5
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
Page 5/5

Try it yourself

Task

Rhombus with \(\overline{BD} = 5\) cm and side \(4\) cm: which radii around \(B\) and \(D\)?

Show solution

Both \(4\) cm.

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: Drachen und Raute (Eigenschaften, Symmetrieachse, Diagonalen, Konstruktion mit dem Zirkel). 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.