Where can you put the mirror across the square so that you can still 'see' the whole square?
How many different positions are possible?
How many lines of symmetry does a square have?

Can you reflect part of the square so that you can see a smaller square?
A rectangle? A kite? A hexagon? An octagon?
What do all the shapes have in common?

This problem has been adapted from the book "Starting from Mirrors" by David Fielker, published by BEAM Education. This book is out of print but can still be found on Amazon.