Question

如图,在四边形ABCD中,AC平分∠BAD,CE⊥AB于点E,且∠B+∠D=180°,求证:AE=AD+BE

Answer 1

证明：过C在AD的延长线上作CF⊥AD,

AC平分∠BAD,CE⊥AD

则△AFC≌△AEC

∠B+∠D=180°,则∠B=∠CDF

∠CFD=∠CEB=90°,CF=CE,

,则△BFC≌△DEC

AF=AE,DF=BE

则 AE=AD+DF=AD+BE