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

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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