Question

if angle A= angle B and AD=BE show that DE ia parallel to AB in triangle ABC

Answer 1

In a ΔABC, D is the point in AC

                  E is the point in BC

∠A=∠B  ;  AD=BE (Given)

∴AC=BC (isosceles triangle)

AD+DC   =    BE+EC

AD+DC    =   AD+EC

∴DC  =  EC

 AD   =  BE

AD/BE =  DC/EC

AD/DC = BE/EC

∴DE║AB (By proportionality)