苏州立达中学分校:选择题(初中)

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在三角形ABC中,EF分别是BC的三等分点,M是AC的中点,BM与AE,BF分别相交于点G,H,则BG:GH:HM= ( )

A 4:3:1 B 4:2:1 C 5:3:1 D 5:3:2

解释一下过程...

在三角形ABC中,EF分别是BC的三等分点,M是AC的中点,BM与AE,AF分别相交于点G,H,则BG:GH:HM= ( )
A 4:3:1 B 4:2:1 C 5:3:1 D 5:3:2
选D 5:3:2
连结MF
则AE平行于MF
因为BE=EF=FC
因此可知
BG:GM=BE:EF=1:1
GE:MF=1:2
MF:AE=1:2
所以MF:AG=2:3
所以MH:HG=MF:AG=2:3
因此BG:GH:HM=5:3:2
选D

c

题出错了 应该是:
在三角形ABC中,EF分别是BC的三等分点,M是AC的中点,BM与AE,AF分别相交于点G,H,则BG:GH:HM= ( )

选 B

ACsg - 助理 二级的结论是对的。

DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD
DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD
DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD
DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD
DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD DDD

D