Question

如图四边形abcd中,ac平分∠bad,ce⊥ab于e,ad ab=2ae 则∠b与∠adc互补,为什么

Answer 1

证明：过C作CF垂直AD于F,

∵AC平分∠BAD,

∴∠FAC=∠EAC,

∵CE⊥AB,CF⊥AD,

∴∠DFC=∠CEB=90°,

∴△AFC≌△AEC,

∴AF=AE,CF=CE,

∵2AE=AB+AD,

又∵AD=AF-DF,AB=AE+BE,AF=AE,

∴2AE=AE+BE+AE-DF,

∴BE=DF,

∵∠DFC=∠CEB=90°,CF=CE,

∴△CDF≌△CEB,

∴∠ABC=∠CDF,

∵∠ADC+∠CDF=180°,

∴∠B+∠ADC=180°．