This problem follows on from Mirror, Mirror...

You might find it helpful to copy this diagram onto squared paper .

Reflect the flag in one of the lines.
Reflect the resulting image in the other line.
Can you describe the single transformation that takes the first flag to the last flag?

Does it matter in which line you reflect first?

Try this with the flag in other positions.

In each case, what is the single transformation that takes the first flag to the last flag?

Now try it with lines that meet at $45^{\circ}$ and at $60^{\circ}$ (you might find it helpful to use isometric paper for the $60^{\circ}$ case).

Again, try it with the flag in different positions

Can you describe the single transformation that takes the first flag to the last flag when the lines meet at $\theta^{\circ}$ (theta degrees)?

If you have enjoyed this problem, you may like to have a go at Who is the fairest of them all? .