To prove BE=DC, first prove △ Abe △ ACD.
Abd and AEC are equilateral triangles, ∴AD=AB,AC=AE, ∠ Bad = ∠ CAE = 60 (∠ 1 = ∠ 2).
∴∠DAC=∠BAE (that is, ∠ 1+∠3=∠2+∠3 in the figure), and prove the congruence of two triangles by the method of edges and corners.
∴△ADC≌△BAE
∴BE=CD
Friend, how can ordinary people solve your four requirements in such detail? You can go to some remedial classes or advanced classes to get this information, or consult your teacher directly. I have several ways to do this topic, you can refer to it: make a relatively accurate picture on the draft paper, mark the known conditions with different symbols, and then look for hidden conditions. Prove that the problem is nothing more than using the condition of triangle congruence, the usage of two parallel, vertical and median vertical lines, the usage of angular bisector and so on. It is generally not difficult to do the problem by adding auxiliary lines appropriately.