如图,已知,点E在AC上且,连结DE并延长它,交BC于点F,交AB的延长线于点G.(1)试说明:△ADE∽△CFE;(2)当时,①求的值和的长;②当点恰好是的中点时,求的长;(3)当的值为多少时-九年

题目简介

如图,已知,点E在AC上且,连结DE并延长它,交BC于点F,交AB的延长线于点G.(1)试说明:△ADE∽△CFE;(2)当时,①求的值和的长;②当点恰好是的中点时,求的长;(3)当的值为多少时-九年

题目详情

如图,已知,点EAC上且,连结DE并延长它,交BC于点F,交AB的延长线于点G.

(1)试说明:△ADE∽△CFE
(2)当时,
①求的值和的长;
②当点恰好是的中点时,求的长;
(3)当的值为多少时,.请简单说明理由.
题型:解答题难度:中档来源:不详

答案

(1)证明见解析(2)①3,6②4(3)3,理由见解析
解:(1)∵
,···················· (2分)
.··························· (3分)
(2)① ∵
.·························· (4分)


.··················· (6分)
② ∵点FBC的中点,
.

.······························ (7分)



.······························ (8分)
由①可知:
.······························ (9分)
(3)当时,.······················· (10分)
理由如下:


,····························· (11分)
.  (12分)
(1)利用平行线的性质求得,从而求得结论
(2)①通过求得结论②通过,求得
得出,从而求解
(3)通过比值求解

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