已知:如图,AD是△ABC的边BC上的中线,AE是△ABD的边上的中线,BA=BD.求证AC=2AE.图:file:///C:/Users/lenovo/AppData/Local/Microsoft/Windows/Temporary%20Internet%20Files/Content.IE5/MIGCZSNK/20091025134035-41792726%5B1%5D.jpg不要
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 04:38:55
![已知:如图,AD是△ABC的边BC上的中线,AE是△ABD的边上的中线,BA=BD.求证AC=2AE.图:file:///C:/Users/lenovo/AppData/Local/Microsoft/Windows/Temporary%20Internet%20Files/Content.IE5/MIGCZSNK/20091025134035-41792726%5B1%5D.jpg不要](/uploads/image/z/8536620-12-0.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A%E5%A6%82%E5%9B%BE%2CAD%E6%98%AF%E2%96%B3ABC%E7%9A%84%E8%BE%B9BC%E4%B8%8A%E7%9A%84%E4%B8%AD%E7%BA%BF%2CAE%E6%98%AF%E2%96%B3ABD%E7%9A%84%E8%BE%B9%E4%B8%8A%E7%9A%84%E4%B8%AD%E7%BA%BF%2CBA%3DBD.%E6%B1%82%E8%AF%81AC%3D2AE.%E5%9B%BE%EF%BC%9Afile%3A%2F%2F%2FC%3A%2FUsers%2Flenovo%2FAppData%2FLocal%2FMicrosoft%2FWindows%2FTemporary%2520Internet%2520Files%2FContent.IE5%2FMIGCZSNK%2F20091025134035-41792726%255B1%255D.jpg%E4%B8%8D%E8%A6%81)
已知:如图,AD是△ABC的边BC上的中线,AE是△ABD的边上的中线,BA=BD.求证AC=2AE.图:file:///C:/Users/lenovo/AppData/Local/Microsoft/Windows/Temporary%20Internet%20Files/Content.IE5/MIGCZSNK/20091025134035-41792726%5B1%5D.jpg不要
已知:如图,AD是△ABC的边BC上的中线,AE是△ABD的边上的中线,BA=BD.求证AC=2AE.
图:file:///C:/Users/lenovo/AppData/Local/Microsoft/Windows/Temporary%20Internet%20Files/Content.IE5/MIGCZSNK/20091025134035-41792726%5B1%5D.jpg
不要用相似
已知:如图,AD是△ABC的边BC上的中线,AE是△ABD的边上的中线,BA=BD.求证AC=2AE.图:file:///C:/Users/lenovo/AppData/Local/Microsoft/Windows/Temporary%20Internet%20Files/Content.IE5/MIGCZSNK/20091025134035-41792726%5B1%5D.jpg不要
∵D是BC中点,
∴BD=DC=BC/2
∵E是BD中点
∴BE=ED=BD/2=BC/4
∵BA=BD=BC/2
∴AB:BC=BE:AB=1:2
∵∠B=∠B
∴△BAE∽△BCA
∴AE:AC=AB:BC=1:2
即AC=2AE
过D点做AB平行线叫AC与F
则根据中位线定理可知
AC=2AF
DF=AB/2=BD/2=DE
在△ADE和△ADF中
AD=AD
∠ADF=∠DAB=∠ADE
DF=DE
△ADE≌△ADF
∴AF=AE
AC=2AE