Question 490853
You will see that, upon drawing D,E,F and forming DEF, that there are three "outer" triangles, and triangle DEF. Each of these "outer" triangles has a 60 degree angle, and its two adjacent sides are 1/2 the length of a side length of ABC; hence the outer three triangles are equilateral. This implies DEF is also equilateral, because the side lengths of DEF are the side lengths of the other three triangles.