## triangle symmetry

*This follows on from shift and swap.*

Start with three people at the corners of an equiliateral triangle. There are six moves:

**L,M,N = reflect in the three different lines of symmetry**

P = rotate 120 degrees clockwise

Q = rotate 120 degrees anticlockwise

I = identity

P = rotate 120 degrees clockwise

Q = rotate 120 degrees anticlockwise

I = identity

This task is adapted from the SMP booklet YE1; click on the image to make it bigger.

pairs of moves. What single moves are they the same as? (suggestion: put the moves in a grid, like a sample space grid and note that order may be important!)2. What moves are opposites (inverses) of each other? What moves are inverses of themselves? How can you recognise pairs of inverses? 3. Do you need all six moves to generate all six positions? 4. Investigate combinations of more than two moves. How can you simplify these combinations? 5. Investigate for other shapes with more sides (eg square, pentagon,...). What other questions can you ask? How can you extend this task? |

After this, you might want to try twisting and turning from NRICH. I tried it with my year 12 students, it was good fun.

Below are my thoughts on this task

*I wonder what would happen if you attached the people in the task above with skipping ropes?*Below are my thoughts on this task