targas-edu.de
DE ☾ A+

Angle bisector

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

You learn the angle bisector (die Winkelhalbierende): it divides an angle into two equal parts. You construct it with compasses.
📄 Open worksheet (PDF, German)

The video

In the video you bisect an angle of \(70^\circ\) with compasses. Then you see a common mistake and an exercise.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:15 Equal distance
  3. 0:33 Construction with compasses
  4. 1:48 Careful, mistake!
  5. 2:10 Try it yourself

The most important points

Angle bisector

The angle bisector \(w\) divides the angle \(\alpha\) into two equal angles. \(70^\circ : 2 = 35^\circ\). Every point on \(w\) has the same distance from both arms (measured at a right angle).

The angle bisector divides 70^\circ into 35^\circ and 35^\circ.
The angle bisector divides \(70^\circ\) into \(35^\circ\) and \(35^\circ\).

Construction with compasses

1. Arc around \(S\): intersections \(P\) and \(Q\) on the arms. 2. Arc around \(P\) with \(r > \frac{PQ}{2}\). 3. Arc around \(Q\) with the same radius: intersection \(R\). 4. Line through \(S\) and \(R\).

The construction of the angle bisector.
The construction of the angle bisector.

Careful: If the compasses are set too small (\(r < \frac{PQ}{2}\)), the arcs do not meet.

Exercise: halving 80^\circ gives 40^\circ.
Exercise: halving \(80^\circ\) gives \(40^\circ\).

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 1/4
The worksheet – Page 2
Page 2/4
The worksheet – Page 3
Page 3/4
Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

Bisect an angle of \(80^\circ\). How big is each half?

Show solution

\(80^\circ : 2 = 40^\circ\).

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: Winkelhalbierende (Eigenschaft, 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.