摘要：21．⑴BE平分∠ABC. ---1分∵CD＝AC.∴∠D=∠CAD. ∵AB＝AC.∴∠ABC=∠ACB∵∠EBC=∠CAD.∴∠EBC=∠D=∠CAD. --------4分∵∠ABC=∠ABE+∠EBC.∠ACB=∠D+∠CAD.∴∠ABE=∠EBC.即BE平分∠ABC. --------6分⑵由⑴知∠CAD=∠EBC =∠ABE. ∵∠AEF=∠AEB.∴△AEF∽△BEA. --------8分

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