Question

如图,在△ABC和△ADE中,AC=AB,AE=AD,∠CAB=∠EAD=90°.求证CE=BD；CE⊥BD.

Answer 1

证明,ΔDAB全等于ΔEAC

理由AC=AB,AE=AD.∠DAB=∠EAC

故CE=BD

设CE与BD交于点O.

有ΔDAB全等于ΔEAC

∠BDA=∠CEA

所以∠ADE+ ∠AED=∠ADB+∠BDE+∠AED=∠AEC+∠BDE+∠AED=∠BDE+∠DEC=90°

即∠DOE=90°

即 CE⊥BD.