I still cannot prove this triangle being similar to the other one, if anyone can explain it that would be extremly grateful.
Picture is linked
Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. In other words, two triangles are similar if they have the same shape.
In this case, the two triangles have different shapes. AED is clearly an equilateral triangle, while ABC is an scalene one, so they aren't similar.