如图,在四边形ABCD中,BD既平分∠ABC,又平分∠ADC,且CB=CD.求证:四边形ABCD是菱形.

∵BD平分∠ABC、∠ADC,∴∠ABD=∠CBD,∠ADB=∠CDB,
又BD=BD,∴ΔABD≌ΔCBD,
∴AB=CB,AD=CD,
∵CB=CD,
∴AB=CB=CD=AD,
∴四边形ABCD是菱形.