Question

In a triangle abc d and e are the points on sides ab and ac respectively such that AD × EC = AE× DB prove that DE parallel to BC

Answer 1

first draw a triangle ABC
draw a point D on AC and E on AC
and then draw DE
proof = draw a perpendicular bisector on BC through A
and then make ABM congruent to ACM
by cpct AB=AC
by proving this D is mid point is AB and E is mid point of AC
So that's why DE parallel to BC