Question

1.已知：如图,在平行四边形ABCD中,AD=2AB,E,F分别是线段BA,AB的延长线上的点,且AE=BF=AB,M,

Answer 1

设EC交AD于M,FD交BC于N

DC//AB,AE=AB=DC

△MDC≡△MAE

MA=MD,MA=1/2AD=AB=AE

∠AEM=∠AME

∠DAF=∠AEM+∠AME=2∠AEM

同理∠CBA=2∠AFD

∠DAF+∠CBA=2∠AEM+2∠AFD=180

∠AEM+∠AFD=90

EC垂直FD