Question

如图,点B,F,C,E在同一条直线上，AC、DF相交于点G，AB⊥BE,垂足为B，DE⊥BE，垂足为E，且AB=DE,AC=DF

如图,点B,F,C,E在同一条直线上，AC、DF相交于点G，AB⊥BE,垂足为B，DE⊥BE，垂足为E，且AB=DE,AC=DF。
求证：①△ABC≌△DEF
②GF=GC
图

Answer 1

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Answer 2

∵BF=CE∴BC=BF+FC=CE+FC=EF
∵AB⊥BC DE⊥BE
∴∠ABC=∠DEF=90度
又∵AB=DE
∴⊿ABC≌⊿DEF(边角边)

在⊿GFC中
∠ACB=∠DEF(全等三角形对应角相等)
∴GF＝GC

Answer 3

证明：1.∵AB=DE,AC=DF，∠ABC=∠DEF，∴△ABC≌△DEF
2.∵△ABC≌△DEF，∴∠ACB=∠DFE，∴GF=GC

Answer 4

没有图。