Question

In the given figure, angleA = angleB and AD=BE show that DE is parallel to AB in triangle ABC.

Answer 1

In the given figure:
AngleB=AngleC
Therefore,triangle ABC is an isosceles tiangle ,then
AC=BC
AD+DC=BE+EC
AD+DC=AD+EC
[As,AD=BE is given]
DC=EC
(Subtracting AD from both sides).
DC/EC=1-------1
Also,it is given that
AD=BE
AD/BE=1-------2
From 1 and 2 ,we have,
AD/BE=DC/EC
AD/DC=BE/EC
Hence, by the converse of basic proportionality theorem "If a line divides any two sides of a triangle in the same ratio,then the line must be parallel to the third side ".
Therefore, DE||AB...

Answer 2

Hope it's useful for u.........