矩形ABCD中,E是AD中点将▷ABE折叠的▷GBE,延长BG交DC于点F,证明GF=DF.(2)若DC=2DF,求AB/AB的值(3)若DC=n*DF,求AD/AB的值
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![矩形ABCD中,E是AD中点将▷ABE折叠的▷GBE,延长BG交DC于点F,证明GF=DF.(2)若DC=2DF,求AB/AB的值(3)若DC=n*DF,求AD/AB的值](/uploads/image/z/4977030-30-0.jpg?t=%E7%9F%A9%E5%BD%A2ABCD%E4%B8%AD%2CE%E6%98%AFAD%E4%B8%AD%E7%82%B9%E5%B0%86%26%239655%3BABE%E6%8A%98%E5%8F%A0%E7%9A%84%26%239655%3BGBE%2C%E5%BB%B6%E9%95%BFBG%E4%BA%A4DC%E4%BA%8E%E7%82%B9F%2C%E8%AF%81%E6%98%8EGF%3DDF.%282%29%E8%8B%A5DC%3D2DF%2C%E6%B1%82AB%2FAB%E7%9A%84%E5%80%BC%EF%BC%883%EF%BC%89%E8%8B%A5DC%3Dn%2ADF%2C%E6%B1%82AD%2FAB%E7%9A%84%E5%80%BC)
矩形ABCD中,E是AD中点将▷ABE折叠的▷GBE,延长BG交DC于点F,证明GF=DF.(2)若DC=2DF,求AB/AB的值(3)若DC=n*DF,求AD/AB的值
矩形ABCD中,E是AD中点将▷ABE折叠的▷GBE,延长BG交DC于点F,证明GF=DF.
(2)若DC=2DF,求AB/AB的值
(3)若DC=n*DF,求AD/AB的值
矩形ABCD中,E是AD中点将▷ABE折叠的▷GBE,延长BG交DC于点F,证明GF=DF.(2)若DC=2DF,求AB/AB的值(3)若DC=n*DF,求AD/AB的值
(1)、连接EF,由题意知,△ABE≌△GBE,E是AD中点
——》EG=EA=ED,
∠EGB=∠EAB=90°,
——》∠EGF=∠EDF=90°,
——》EF=EF,
——》RT△EGF≌RT△EDF(HL),
——》GF=DF;
(3)、DC=nDF,——》CF=DC-DF=(n-1)DF,
BG=AB=DC=nDF,——》BF=BG+GF=(n+1)DF,
——》AD=BC=v(BF^2-CF^2)=2vnDF,
——》AD/AB=2vn/n,
(2)、将n=2代入上式,
得:AD/AB=2v2/2=v2.