四边形ABCD中,AD‖BC,E在BC上,F在CD上,∠AEF=∠ACD,∠BAC=∠D 求证:AB/BC=AE/EF

Question

四边形ABCD中,AD‖BC,E在BC上,F在CD上,∠AEF=∠ACD,∠BAC=∠D 求证:AB/BC=AE/EF

Answer 1

证明：设AC与EF的交点为O, 连接EF
∵∠1=∠2,∠AOE=∠COF
∴△AOE∽△COF
∴AO/OE=OF/OC
∵∠AOF=∠COE
∴△AOF∽△EOC
∴∠AFE=∠ACB
∵AD‖BC
∴∠CAD=∠ACB
∵∠BAC=∠D
∴∠B=∠2
∴∠B=∠1
∴△ABC∽△AEF
∴AE/EF=AB/BC