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Constructing a triangle: ASA

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

You construct a triangle from one side and the two angles at this side (WSW).
📄 Open worksheet (PDF, German)

The video

The video shows every step with the set square and the compasses. The given parts are pink in the sketch.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:17 The sketch
  3. 0:28 The side c
  4. 0:34 The angles
  5. 1:05 Labelling
  6. 1:13 The description
  7. 1:49 Careful, mistake!
  8. 2:13 Try it yourself

The most important points

First draw a sketch (die Planfigur) without exact measurements. Mark what is given.

How to construct

1. Draw \(c\) with \(A\) and \(B\). 2. Draw the angle \(\alpha\) at \(A\) on \(c\) (outer scale). 3. Draw the angle \(\beta\) at \(B\) on \(c\) (inner scale). 4. The intersection of the arms is \(C\).

The finished triangle: c = 6 cm, \alpha = 40^\circ, \beta = 70^\circ.
The finished triangle: \(c = 6\) cm, \(\alpha = 40^\circ\), \(\beta = 70^\circ\).

Remember

One side and the two adjacent angles: exactly one triangle. Congruence rule WSW (angle – side – angle).

The construction description in four lines.
The construction description in four lines.
Mistake: \beta read on the outer scale – 110^\circ instead of 70^\circ.
Mistake: \(\beta\) read on the outer scale – \(110^\circ\) instead of \(70^\circ\).

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

Given: \(c = 5\) cm, \(\alpha = 60^\circ\), \(\beta = 50^\circ\). Which scale do you use at \(A\)? Which at \(B\)?

Show solution

At \(A\): outer scale. At \(B\): inner scale.

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: Dreiecke konstruieren nach WSW (Planfigur, Winkel antragen mit dem Geodreieck, äußere und innere Maßskala). 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.