证明:(1)连接 C交A 于点O,连接OD在△ BC中, ∵点D是BC的中点,O是 C的中点 ∴ B∥OD ∵OD 平面AD , B 平面AD ; ∴ B∥平面AD ; (2)直三棱柱ABC﹣![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022002259-80306.png) ![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022002259-17289.png) 中, C⊥平面ABC ∴ C⊥AD 在△ABC中,AD⊥BC ∵BC∩ C=C ∴AD⊥平面BC![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022002300-48492.png) ![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022002301-44173.png) 连接DE, ∵E是![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022002301-60305.png) 的中点 ∴四边形 BDE为平行四边形 ∴ B∥ED, B=ED ∵ B∥ A, B= A ∴ED∥ A,ED= A ∴四边形 ADE为平行四边形 ∴ E∥AD ∴ E⊥平面BC![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022002304-58189.png) ![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022002304-34801.png) ∵ E 平面 BE ∴平面 BE⊥平面BC![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022002306-15923.png) . |