如图所示,已知AC与BD相交于E,AE=AB-1,AE=DC,AD=BE,∠ADC=∠DEC,则EC=_.
问题描述:
如图所示,已知AC与BD相交于E,AE=AB-1,AE=DC,AD=BE,∠ADC=∠DEC,则EC=______.
答
∵AE=DC,AD=BE,又∠AEB=∠DEC=∠ADC,
∴△AEB≌△CDA,∴AB=AC,
又AE=AB-1=AC-1=AC-CE,
∴CE=1.
故答案为1.