Question

如下页图,点D，E在三角形ABC的边BC上，AB等于AC,AD等于AE.求证BD等于CE

Answer 1

因AC=AB
所以角B=角C
因AE=AD
所以角AEC=角ADB
根据角C=角渗携B,角AEC=角ADB,AC=AB（角角边）
得三角形AEC与三角丛腔伏圆敏形ADB全等，所以CE=BD

Answer 2

因尘念为，AB=AC所以，角B=角C因孙并为，AD=AE所派凯困以，角ADB=角AEC所以，角BAD=角CAE所以，三角形BAD全等于三角形CAE所以，BD=CE

Answer 3

∵AD=AE∴∠AED=∠闹梁ADE又∵AB=AC∴∠液唤运B=∠C又∵AB=AC∴△ACD≌△ABE∴CD=BE又链告∵CE=CD-DE,BD=BE-DE∴BD=CE

Answer 4

∵AB=AC∴∠ABC=∠ACB∵AD=AE∴∠ADC=∠AEB∴扒念世∠ADB=∠AEC∴△ADB≌△春肢AEC∴高拦BD=CE