$\because \angle 1=\angle C$，$(已知)$
$\therefore GD$∥$AC.(同位角相等，两直线平行)$
$\therefore \angle 2=\angle DAC.(两直线平行，内错角相等)$
$\because \angle 2+\angle 3=180^{\circ}$，（已知）
$\therefore \angle DAC+\angle 3=180^{\circ}.(等量代换)$
$\therefore AD$∥$EF.(同旁内角互补，两直线平行)$
$\therefore \angle ADC=\angle EFC.(两直线平行，同位角相等)$
$\because EF\bot BC$，$(已知)$
$\therefore \angle EFC=90^{\circ}.(垂直的定义)$
$\therefore \angle ADC=90^{\circ}.(等量代换)$
故答案为：$AC$；同位角相等，两直线平行；两直线平行，内错角相等；同旁内角互补，两直线平行；$\angle EFC$；垂直的定义.

$\because \angle 1=\angle C$，$(已知)$
$\therefore GD$∥$AC.(同位角相等，两直线平行)$
$\therefore \angle 2=\angle DAC.(两直线平行，内错角相等)$
$\because \angle 2+\angle 3=180^{\circ}$，（已知）
$\therefore \angle DAC+\angle 3=180^{\circ}.(等量代换)$
$\therefore AD$∥$EF.(同旁内角互补，两直线平行)$
$\therefore \angle ADC=\angle EFC.(两直线平行，同位角相等)$
$\because EF\bot BC$，$(已知)$
$\therefore \angle EFC=90^{\circ}.(垂直的定义)$
$\therefore \angle ADC=90^{\circ}.(等量代换)$
故答案为：$AC$；同位角相等，两直线平行；两直线平行，内错角相等；同旁内角互补，两直线平行；$\angle EFC$；垂直的定义.