Reflecting Squarely

In how many ways can you fit all three pieces together to make shapes with line symmetry?

There are more than five solutions to this problem - how many can you find?

Can you find them all?

Additional printable copies of the shapes can be found here.

Try changing the question a bit:

For example, design your own set of three shapes (drawn on a square grid, as above), keep the total area 10. How many ways can they be arranged to make symmetrical shapes?
Can you find a set of three such shapes, which have more valid arrangements than the shapes from the original problem?
Can you find three such shapes which can never be arranged to make a symmetrical shape?

This problem is based on one found in the Dime "Line Symmetry A" pack, produced by Tarquin Publications

A poster of this problem is available here.