Question

ab平行cd,ec,eb分别平分角bcd和角cba,点e在ad上,求证:bc=ab+cd

Answer 1

证明：在BC上取BF=BA,易证明△ABE≌△FBE,∴AB=FB,∠AEB=∠FEB,又EB、EC是角平分线,且AB∥DC,∴易求∠BEC=90°,∴∠AEB＋∠DEC=90°,∴∠FEC=∠DEC,EC=EC,∠FCE=∠DCE,∴△FCE≌△DCE,∴FC＝DC,∴BC=AB＋DC