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

Question

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

Tanveer Sofi · Accepted Answer

In the given figure:∠B=∠CTherefore, triangle ABC is an isosceles triangle, then       AC=BC⇒AD+DC=BE+EC⇒AD+DC=AD+EC              As, AD=BE  is given⇒DC=EC                                     Subtracting AD from both sides
⇒DCEC=1                                     
IAlso it is given thatAD=BE⇒ADBE=1                                     
IIFrom  I  and  II, we haveADBE=DCEC⇒ADDC=BEECHence, 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