If AD/DB = AE/EC, then line segment DE is parallel to line segment BC.
In Mathematics and Euclidean Geometry, the basic proportionality theorem states that when any of the two sides of a triangle is intersected by a straight line which is parallel to the third side of the triangle, then, the two sides that are intersected would be divided proportionally and in constant ratio.
Note: AB = AD + DB
AC = AE + EC
By applying the basic proportionality theorem to isosceles triangle ABC, we have the following proportional side lengths:
DE ║ EC
AD/DB = AE/EC (line segment DE divides segment AB and AC in the same ratio)
In conclusion, we can logically deduce that line segment DE is parallel to line segment BC.