Description/Aim

Look at quadrilaterals like you never have done before! Using dynamic geometry (geogebra) or the java applet below, experiment with the limits of the quadrilaterals, determine which is which and then which quadrilateral is a subset of which other quadrilateral. Work towards a quadrilateral Venn diagram the tells the whole truth!

Please find below, the digital worksheet, a geogebra file and a link to the same file as a java applet.

Time 1- 2 hours Age 14+

Why we like this activity ….

The challenging of preconceptions! Another fine example of dynamic geometry opening doors to
discovery and experimetation. Students start arguing about statements like 'all squares are rectangles'
and end up constructing a complex Venn diagram!

How this activity be used ….

Obviously students will need to be at their computers to really get stuck into this task. My choice would
be one each with discussion between neighbours, but this is easily done in pairs or groups

What to expect when using this activity – from our experience

Some good debate! some confusion and some frustration! The last part of the task is really challenging.
It is not essential that they get to the end. It is probably enough that they understand that squares are a
subset of rectangles and rectangles are a subset or parallelograms for example.

Extra Notes

Depending on time and students, the activity could begin with asking students to construct the
quadriltaerals. This is done in 'Constructing Quadrilaterals'

Written by J. Noble 24th March 2009 (c)

Credit to Richard Keeping who first showed me the final diagram and David Harris whose activity this
one is based on.