Question

如图，AC=BC,CE=CD,∠ACB=∠DCE=90°

1.请在图中找出一对全等三角形，加以证明
2.求证：BE⊥AD

Answer 1

⊿ACD≌⊿BCE
∵∠ACB=∠DCE=90°
∴∠ACD=∠BCE
∵AC=BC,CE=CD
∴⊿ACD≌⊿BCE﹙SAS﹚
∴∠ADC=∠CBE
∵∠DCE=90°
∴∠CDE+∠CED=90°
∴∠CDE+∠CBE+∠BED
=∠CDE+∠BDC+∠BED
=∠BDE+∠BED
∴∠DBE=90°
即BE⊥AD