Question

问一个关于四边形的题目如图,已知在四边形ABCD中,AD⊥DC,BC⊥AB,AE平分∠DAB,CF平分∠DCB,AE交C

Answer 1

∵AD⊥DC,BC⊥AB,

∴∠D=∠B=90°．

∵∠DAB+∠B+∠BCD+∠D=360°,

∴∠DAB+∠BCD=180°．

∵AE平分∠BAD,CF平分∠DCB,

∴∠DAE+∠DCF=90°．

∵∠D+∠DFC+∠DCF=180°,

∴∠DFC+∠DCF=90°．

∴∠DAE=∠DFC

∴AE∥CF．