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每日小编都会为大家带来一些知识类的文章，那么今天小编为大家带来的是","title_text":"方面的消息知识，那么如果各位小伙伴感兴趣的话可以，认真的查阅一下下面的内容哦。

（1）.【答案】

$left(1right)$见解析；$left(2right){60}^{circ }$;$left(3right)HF=dfrac{1}{2}CF$

【解析】

（1）$because triangle ABC$是等边三角形

$therefore AB=AC$,$angle ABC=angle BAC=angle ACB={60}^{circ }$

在$triangle ABD$和$triangle CAE$中

$left{begin{array}{l}AB=CA angle B=angle EAC BD=AEend{array}right.$

$therefore triangle ABDykcong triangle CAEleft(SASright)$

$therefore AD=CE$

（2）由（1）可知，$triangle ABDykcong triangle CAE$

$therefore angle BAD=angle ACE$

$because angle DFC$是$triangle ACF$的外角

$therefore angle DFC=angle FAC+angle ACE=angle FAC+angle BAD=angle BAC={60}^{circ }$

故$angle DFC= 60{}^{circ } $

（3）$because CHbot AD$

$therefore angle FHC= 90{}^{circ } $

$therefore triangle CFH$是直角三角形

由（2）可知，$ angle DFC={60}^{circ }$

$therefore angle FCH=180{}^{circ } - angle FHC- angle DFC = 180{}^{circ } -90{}^{circ }- 60{}^{circ } = {30}^{circ }$

$therefore HF=dfrac{1}{2}CF$

（2）.【答案】

相等的边：$AB=BC=AC$，$CD=DE=CE$，$BD=AE$，$BM=AN$，$MD=NE$，$MC=MN=CN$

相等的角：$angle ABC=angle BAC=angle ACB=angle MCN=angle NMC=angle MNC=angle DCE=angle DEC=angle CDE={60}^{circ }$，$angle CAE=angle CBD$，$angle BDC=angle AEC$，$angle BCD=angle ACE$，$angle DMC=angle AMB=angle ENC=angle AND$，$angle BMC=angle AMD=angle ANC=angle DNE$

全等三角形：$triangle BCDykcong triangle ACE$，$triangle BCMykcong triangle ACN$，$triangle DCMykcong triangle ECN$

平行关系：$ABykparallel CD$，$ACykparallel DE$，$MNykparallel BE$

等边三角形：$triangle ABC$，$triangle DCE$，$triangle MCN$

【解析】

$because triangle ABC$和$triangle DCE$是等边三角形

$therefore AB=BC=AC$，$CD=DE=CE$,

$angle ABC=angle BAC=angle ACB={60}^{circ }$，$angle DCE=angle DEC=angle CDE={60}^{circ }$

$therefore angle ACB+angle MCN=angle DCE+angle MCN$

即$angle BCD=angle ACE$

在$triangle BCD$和$triangle ACE$中

$left{begin{array}{l}BC=AC angle BCD=angle ACE CD=CEend{array}right.$

$therefore triangle BCDykcong triangle ACE$$left(SASright)$

$therefore BD=AE$，$angle CAE=angle CBD$，$angle BDC=angle AEC$

$because angle MCN={180}^{circ }-angle ACB-angle DCE={60}^{circ }$

$therefore angle ACB=angle MCN=angle DCE={60}^{circ }$

在$triangle BCM$和$triangle ACN$中

$left{begin{array}{l}angle CBD=angle CAE BC=AC angle BCM=angle ACNend{array}right.$

$therefore triangle BCMykcong triangle ACN$$left(ASAright)$

$therefore MC=NC$，$BM=AN$，$angle BMC=angle ANC$

$therefore angle BMC=angle AMD=angle ANC=angle DNE$

同理$triangle DCMykcong triangle ECN$$left(ASAright)$

$therefore MD=NE$，$angle DMC=angle ENC$

$therefore angle DMC=angle AMB=angle ENC=angle AND$

$because MC=NC$，$angle MCN={60}^{circ }$

$therefore triangle MCN$为等边三角形

$therefore MC=MN=CN$，$angle MCN=angle CMN=angle CNM={60}^{circ }$

$therefore angle ABC=angle DCE={60}^{circ }$，$angle ACB=angle DEC={60}^{circ }$，$angle MNC=angle DCE={60}^{circ }$

$therefore ABykparallel CD$，$ACykparallel DE$，$MNykparallel BE$

本文到此结束，希望对大家有所帮助。