Any line which passes though the centre of the square divides the square into two congruent shapes. An example is shown below.

There are an infinite number of suitable lines (lines passing through the centre, at any angle) so there are infinitely many ways the square can be cut in half with a single straight cut.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.