Question

如图，分别在△ABC的AB、AC两边上向外作正方形ABDE和ACFG，连接EC、BG.判断EC、BG的大小关系？试说明理由。

Answer 1

解：EC = BG
理由：在正方形ABDE     AE = AB        ∠EAB = 90°
        又在正方形ACFG      AG = AC       ∠GAC = 90°
         ∴∠EAB = ∠GAC = 90°
        ∵∠EAC = ∠EAB + ∠BAC ∠GAB = ∠GAC + ∠BAC
        ∴∠EAC =∠GAB
        ∴△EAC≌△GAB
        ∴EC = GB