Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are constructed such that none of these triangles overlaps triangle ABC.
a) Draw a triangle ABC and then sketch the remainder of the figure. It will help if triangle ABC is not isosceles (or equilateral).
b) Show that, regardless of choice of triangle ABC, we always have AX = BY = CZ.
You must include a diagram for any complicated geometry problem that does not come with its own diagram. Diagrams are extremely important in geometry because they help your reader understand what is going on. Diagrams also help you to keep track of your work and possibly give you useful insight.