Thebault's theorem

Victor Thebault is credited with this theorem (1930)

create two equilateral triangles
on two adjacent sides of a square

join the three points as shown

prove that this (red dotty) triangle must be an equilateral triangle











you can do this by considering:
angles and establishing congruence;

or by other methods

what happens if the two triangles are drawn inside rather than outside the square?