题目内容
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,.请简单说明理由.
(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.
(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F是BC的中点,
∴.
∵,
∴.······························ (7分)
∵,
∴,
∴
∴.······························ (8分)
由①可知:,
∴.······························ (9分)
(3)当时,.······················· (10分)
理由如下:
∵,
∴
即,····························· (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
∴,,···················· (2分)
∴.··························· (3分)
(2)① ∵,
∴.·························· (4分)
∵,
∴,
∴,.··················· (6分)
② ∵点F是BC的中点,
∴.
∵,
∴.······························ (7分)
∵,
∴,
∴
∴.······························ (8分)
由①可知:,
∴.······························ (9分)
(3)当时,.······················· (10分)
理由如下:
∵,
∴
即,····························· (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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