Just prove that the two opposing groups are equal.

It is proved that in △BDE and △BAC,

BD = AB

BE=AC

∠DBE=60 - ∠EBA=∠ABC

∴△bde?△BAC

∴ Germany =AC=AF

The same can be proved: DA=EF.

∴ Quadrilateral ADEF is a parallelogram

(2) It has just been proved that the quadrilateral ADEF is a parallelogram. In order to make the quadrilateral ADEF rectangular,

Only one angle is a right angle. If I let ∠ daf = 90.

∠∠DAB =∠FAC = 60

∴∠BAC = 360- 120-90 = 150

∴ To make the quadrilateral ADEF rectangular, you need ∠ BAC = 150.

(3) The quadrilateral ADEF does not necessarily exist for any triangle ABC, because there are only three points when the triangle ABC is an equilateral triangle, so there is no quadrilateral adef at this time.