Question

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

Answer 1

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。

Answer 2

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