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Constructing a triangle: SSA

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 two sides and an angle that is not between them (SsW).
📄 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. 0:31 The side c
  4. 0:36 Angle and arc
  5. 1:03 Labelling
  6. 1:09 The description
  7. 1:50 Careful: two triangles
  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 \(\beta\) at \(B\) on \(c\), long arm. 3. Arc around \(A\) with radius \(b\): this gives \(C\). 4. Join \(A\) to \(C\).

The finished triangle: c = 5 cm, b = 6 cm, \beta = 70^\circ.
The finished triangle: \(c = 5\) cm, \(b = 6\) cm, \(\beta = 70^\circ\).

Remember

If the angle is opposite the longer side: exactly one triangle (SsW). Otherwise maybe two or none.

The construction description in four lines.
The construction description in four lines.
Angle opposite the shorter side: two intersections, two triangles.
Angle opposite the shorter side: two intersections, two triangles.

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: \(b = 5\) cm, \(c = 7\) cm, \(\gamma = 80^\circ\). Is there exactly one triangle?

Show solution

Yes: \(\gamma\) is opposite the longer side \(c = 7\) cm.

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: Dreiecke konstruieren nach SsW (der Winkel liegt der größeren Seite gegenüber, sonst zwei oder kein Dreieck). 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.