Question

OE平分∠AOB，EC⊥OA于C，ED⊥OB于D。求证：OE垂直平分CD

Answer 1

证明：在△OCE和△ODE中∠COE=∠DOE∠OCE=∠ODE=90°OE=OE所以△OCE≌△ODE所以OC=OD不妨设CD、OE相交于F点则在△OCF和△ODF中OC=ODOF=OF∠AOE=∠BOE所以△OCF≌△ODF所以CF=FD,∠OFC=∠OFD 又∠OFC=∠OFD所以∠OFC=∠OFD=90°所以OE垂直平分CD

Answer 2

∠AOE=∠BOE ∠ECO=∠EDO OE=OE △COE≌△DOE OC=OD设CD与OE交于F OC=OD ∠AOE=∠BOE OF=OF △OCF≌△ODF CF=DF ∠CFO=∠DFO 又两角相加180°，则各为90°

Answer 3

三角形0CE和三角形0ED中＜OCE=＜ODE=90度你还要我们证＜OEC=＜OE...