Question

已知：如圖，AB=AE,∠1=∠2,∠B=∠E.

求證：BC=ED.

 

 

Answer 1

見(jiàn)解析

【解析】分析：要證BC=ED,需證△ABC≌△AED.

證明：因?yàn)?/span> ∠1=∠2,

所以 ∠1+∠BAD=∠2+∠BAD,即∠BAC=∠EAD.

又因?yàn)?/span> AB=AE,∠B=∠E,

所以 △ABC≌△AED,

所以 BC=ED.

點(diǎn)撥：已知一邊一角對(duì)應(yīng)相等證兩三角形全等時(shí)，思路有三種：（1）證對(duì)應(yīng)角的另一邊對(duì)應(yīng)相等，“湊”SAS；（2）證對(duì)應(yīng)邊的對(duì)角對(duì)應(yīng)相等，“湊”AAS；（3）證對(duì)應(yīng)邊的另一鄰角對(duì)應(yīng)相等，“湊”ASA.