一梯形ABCD,AD//CD,AD+BC =DC,E为AB中点,求角DEC?不好意思,上题有误,应是梯形ABCD,AD//BC,AD+BC =DC,E为AB中点,求角DEC?

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一梯形ABCD,AD//CD,AD+BC =DC,E为AB中点,求角DEC?不好意思,上题有误,应是梯形ABCD,AD//BC,AD+BC =DC,E为AB中点,求角DEC?

一梯形ABCD,AD//CD,AD+BC =DC,E为AB中点,求角DEC?不好意思,上题有误,应是梯形ABCD,AD//BC,AD+BC =DC,E为AB中点,求角DEC?
一梯形ABCD,AD//CD,AD+BC =DC,E为AB中点,求角DEC?
不好意思,上题有误,应是
梯形ABCD,AD//BC,AD+BC =DC,E为AB中点,求角DEC?

一梯形ABCD,AD//CD,AD+BC =DC,E为AB中点,求角DEC?不好意思,上题有误,应是梯形ABCD,AD//BC,AD+BC =DC,E为AB中点,求角DEC?
延长DE交CB延长线于F,连接CE 因为AE=BE,∠EAD=∠EBF,∠EDA=∠EFB 所以△AED≌△BEF 所以BF=AD,DE=EF 所以AD+BC=BF+BC=CF=DC 又E为DF中点 所以CE垂直平分DF 所以角DEC=90°