Making Indestructible Quadrilaterals

'Construct your own indestructible quadrilaterals based on your understanding of their fundamental properties'

This is an activity in its own right, but does follow on really nicely from Indestructible Quadrilaterals and this will certainly help you to reflect on the defining features of these shapes. So, before you start it is key to be familiar with the properties of quadrilaterals. What is a Rectangle, a Square, Rhombus, Parallelogram, Trapezium/Trapezoid, Kite? How would you describe it to someone as precisely as you can? When is a Rectangle also a Square? These questions and more are at the centre of this activity. Your challenge here is to use dynamic geometry to construct the different quadrilaterals. You must be able to move the points and change the size and dimensions of the shape without changing the shape that it is. The Indestructible Quadrilaterals activity has examples of these shapes and a further example of all seven quadrilaterals is shown below. Try pushing and pulling them! Your task is to recreate them.


Please find below an applet showing 7 indestructible quadrilaterals and a video tutorial on some of the basics for constructing with Geogebra. You will need Dynamic Geometry software and this can be downloaded free from


Video tutorial


  • Explore the examples of Indestructible Quadrilaterals above or those in the Indestructible Quadrilaterals activity.
  • Make sure you understand the fundamental properties of Quadrilaterals
  • Watch the video tutorial on constructions
  • Make and test your own!
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