Draw a right-angled triangle $ABC$, and mark a point $\frac13$ of the way along $AB$, $\frac13$ of the way along $BC$ and $\frac13$ of the way along $CA$.

Join your three points together to form a new triangle.

Try a few examples. What do you notice?

Can you explain why?

We started with a right-angled triangle... what about other triangles?

What fraction of the triangle is shaded purple?

Can you prove it?