梯形abcd,ad平行于bc,ab=dc=ad,bd=bc,设角dbc=x度

DE=DC
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AB=AD => △BAD是等腰三角形,∠ABD=∠ADB
BD=BC => △CBD是等腰三角形,∠BCD=∠BDC
AD‖BC => ∠ADB=∠DBC=∠ABD
AB=DC => 梯形ABCD是等腰梯形,∠ABC=∠BCD=∠BDC=2*∠DBC
DE平分∠BDC => ∠BDE=∠EDC=∠DBC=∠ADB => AB‖DE
所以四边形ABED是菱形,AB=DE=DC=BE=AD
故△BED △EDC也是等腰三角形