$解:(1)如图①,点D_{1}、D_{2}、D_{3} 即为所求$
$(2)\because \angle ABC=80^{\circ}，对角线BD平分\angle ABC，$
$\therefore \angle ABD=\angle DBC=40^{\circ}，$
$\therefore \angle A+\angle ADB=140^{\circ}，$
$\because \angle ADC=140^{\circ}，$
$\therefore \angle BDC+\angle ADB=140^{\circ}，$
$\therefore \angle A=\angle BDC，$
$\therefore \triangle ABD∽\triangle BDC，$
$\therefore BD是四边形ABCD的“相似对角线”$（更多请点击查看作业精灵详解）
