Theorem 6.2 NCERT Class 10 Maths Chapter 6 Triangles
If a line dives the two sides of the triangle in equal ratio, the line is parallel to the third side of the triangle.
if AD/DB = AE/EC, then DE ∥ BC.
Let us assume that DE is not parallel, instead DE’ is parallel to BC.
So as per theorem 6.1, AD/DB = AE’/E’C’. But in theorem 6.2 AD/DB = AE/EC. This is possible when E’ coincides with E. Hence we can say that line DE ∥ BC.