Task F

Propose further extensions of this investigation.

As you worked through the task - you will notice that I have posed many questions that leave much room for both proof and investigation.

One further suggestion is:

Explore the relationship (if any) between triangles made by joining the critical points of the externally (or internally) constructed triangles and the original triangles. Consider - when we constructed external equilateral triangles (and internal ones for that matter) then the triangle formed by joining the centroids was also equilateral (Napoleon's triangle). Will this be the case for the isosceles triangles also and are we limited to the centroid??