Indestructible Quadrilaterals
'Push, pull and stretch these shapes to find out which quadrilaterals they are!'
Each of the shapes in this activity have been carefully constructed so that there are some properties that it ALWAYS has, some properties that it can SOMETIMES have and others that it NEVER has. Your job is push, pull and stretch the shapes any which way you can so you can figure out what these properties are and which shape is which. Once you have done that you are challenged to make your own 'Indestructible Quadrilaterals' using dynamic geometry! A further activity asks you to think about which quadrilaterals are subsets of which other ones. For example, can we say 'All squares are rectangles?' Which other statements like this can we make? This activity should really get you thinking about the properties of different quadrilaterals! Check out 
Quadrilateral Properties as well!
A quick overview
The following screencast gives you a quick overview of this activity by showing some examples.
Resources
Part 1
Keep track of what you discover with this 
Indestructible Quadrilaterals record sheet. The main exercise is then discover which of the following dynamic shapes is a Square, Rhombus, Rectangle, Parallelogram, Kite, Trapezium/Trapezoid and an irregular quadrilateral. 
Shape 1 is below, then follow the links to Shape 2, 
Shape 3, Shape 4, Shape 5, Shape 6 and Shape 7! They are colour coded as well to help.
BE CAREFUL - There is some disagreement about the defining properties of a Trapezium/Trapezoid. The disagreement is about whether or not the shape has 'Exactly' one pair of parallel sides or 'At least' one pair of parallel sides. Read more here 
Trapezium/Trapezoid
Part 2
If you have managed all of the above then follow this link to the Make your own indestructible quadrilaterals page and try making your own using dynamic geometry software. The examples in this activity were all made with the free and versatile Geogebra software.
Part 3
If you are up for an extra challenge then try the problems posed here in this Sets of quadrilaterals worksheet! You will need your answers to part 1 and maybe some of the shapes you made in part 2.
Shape 1
Here is the first of the shapes you need to work with (the others are all on new pages linked to from the menu on the left and the resources section above). Move the shape around and try to put the properties and shapes under the one of the headings, 'Always', 'Sometimes' and 'Never'
Description
- Start with 'Shape 1' on this page (above), move the shape around to see what properties it has 'Always', 'Sometimes' and 'Never'. Put the properties and shapes in the correct columns.
- Take screenshots of the work and keep them in the record sheet.
- Repeat for Shapes 2 through to 7 and fill in the table saying which shape is which.
- Go to the Make your own page and try making your own!
- Try the 'Sets of Quadrilaterals' worksheet to try and summarise the activity.