如图,在四边形ABCD中,BC>BA,AD=DC,BD平分∠ABC. 求证:∠BAD+∠C=180°.
问题描述:
如图,在四边形ABCD中,BC>BA,AD=DC,BD平分∠ABC.
求证:∠BAD+∠C=180°.
答
证明:在BC上截取BE=BA,连接DE,∵BD平分∠ABC,∴∠ABD=∠EBD,在△ABD和△EBD中AB=BE∠ABD=∠EBDBD=BD∴△ABD≌△EBD,∴∠A=∠BED,AD=DE,∵AD=DC,∴DE=DC,∴∠C=∠DEC,∵∠BED+∠DEC=∠A+∠DEC=∠A+C=18...