如图,在△ABC中,AB=AC,∠A=90,∠ACB的平分线CD交AB于点E,∠BDC=90 求证:CE=2BDhttp://hiphotos.baidu.com/%D2%BB%CF%C4%CD%DF%B0%AE%BB%F9/pic/item/ae5c22d0bc8ea97810df9b2d.jpg
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/28 06:45:03
![如图,在△ABC中,AB=AC,∠A=90,∠ACB的平分线CD交AB于点E,∠BDC=90 求证:CE=2BDhttp://hiphotos.baidu.com/%D2%BB%CF%C4%CD%DF%B0%AE%BB%F9/pic/item/ae5c22d0bc8ea97810df9b2d.jpg](/uploads/image/z/2561491-19-1.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%9C%A8%E2%96%B3ABC%E4%B8%AD%2CAB%3DAC%2C%E2%88%A0A%3D90%2C%E2%88%A0ACB%E7%9A%84%E5%B9%B3%E5%88%86%E7%BA%BFCD%E4%BA%A4AB%E4%BA%8E%E7%82%B9E%2C%E2%88%A0BDC%3D90+%E6%B1%82%E8%AF%81%EF%BC%9ACE%3D2BDhttp%3A%2F%2Fhiphotos.baidu.com%2F%25D2%25BB%25CF%25C4%25CD%25DF%25B0%25AE%25BB%25F9%2Fpic%2Fitem%2Fae5c22d0bc8ea97810df9b2d.jpg)
如图,在△ABC中,AB=AC,∠A=90,∠ACB的平分线CD交AB于点E,∠BDC=90 求证:CE=2BDhttp://hiphotos.baidu.com/%D2%BB%CF%C4%CD%DF%B0%AE%BB%F9/pic/item/ae5c22d0bc8ea97810df9b2d.jpg
如图,在△ABC中,AB=AC,∠A=90,∠ACB的平分线CD交AB于点E,∠BDC=90 求证:CE=2BD
http://hiphotos.baidu.com/%D2%BB%CF%C4%CD%DF%B0%AE%BB%F9/pic/item/ae5c22d0bc8ea97810df9b2d.jpg
如图,在△ABC中,AB=AC,∠A=90,∠ACB的平分线CD交AB于点E,∠BDC=90 求证:CE=2BDhttp://hiphotos.baidu.com/%D2%BB%CF%C4%CD%DF%B0%AE%BB%F9/pic/item/ae5c22d0bc8ea97810df9b2d.jpg
如图,在△ABC中,AB=AC,∠A=90,∠ACB的平分线CD交AB于点E,∠BDC=90,
求证:CE=2BD
证明:∵线段CD是∠CDA的平分线
∴AE/BE=AC/BC=1:√2
设AE为1,则BE=√2,AC=1+√2
∴CE=√(AE^2+AC^2)=√[1^2+(1+√2)^2]=√(4+2√2)
又∵ΔBDE∽ΔCAE
∴BD/BE=AC/CE
∴BD=BE*AC/CE=(√2)*(1+√2)/[√(4+2√2)]=[√(2+√2)]/(√2)
∴2BD=2*[√(2+√2)]/(√2)=(√2)*[√(2+√2)]=√(4+2√2)=CE
∴CE=2BD
证毕