在梯形ABCD中,AD//BC,AB垂直于AC,角B等于45度,AD=根2,BC=4根2,求DC的长
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/17 15:42:50
![在梯形ABCD中,AD//BC,AB垂直于AC,角B等于45度,AD=根2,BC=4根2,求DC的长](/uploads/image/z/3949422-6-2.jpg?t=%E5%9C%A8%E6%A2%AF%E5%BD%A2ABCD%E4%B8%AD%2CAD%2F%2FBC%2CAB%E5%9E%82%E7%9B%B4%E4%BA%8EAC%2C%E8%A7%92B%E7%AD%89%E4%BA%8E45%E5%BA%A6%2CAD%3D%E6%A0%B92%2CBC%3D4%E6%A0%B92%2C%E6%B1%82DC%E7%9A%84%E9%95%BF)
在梯形ABCD中,AD//BC,AB垂直于AC,角B等于45度,AD=根2,BC=4根2,求DC的长
在梯形ABCD中,AD//BC,AB垂直于AC,角B等于45度,AD=根2,BC=4根2,求DC的长
在梯形ABCD中,AD//BC,AB垂直于AC,角B等于45度,AD=根2,BC=4根2,求DC的长
作AH⊥BC,垂足H,DE⊥BC,垂足E,
〈B=45°,〈BAC=90°,
°△ABC是等腰RT△,
BC=4√2,
AH=BC/2=2√2,
四边形ADEH是矩形,
EH=AD,DH=AH=2√2,
BH=AH=2√2,HE=AD=√2,
CE=BC-BH-EH=√2,
根据勾股定理,
∴CD^2=DE^2+CE^2=10.
CD=√10.
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