Three segments are drawn from opposite corners of a hexagon

(1) and (2), in different ways, both state that the polygon is a regular hexagon. If this is the case, then the interior angles add up to 180(n-2), or 720. 720/6 = 120. each of these angles is bisected by a segment (the segments that form the 6 triangles), so each of those angles is 60 deg.

Now, the angles that are formed by the intersection of the triangle-forming segments must add up to 360 (because they go all the way around the circle/hexagon). 360/6 = 60

So, we know that all three angles of each triangle are 60 deg, which makes them equilateral. Both are SUFFICIENT

Answer is D.