证明:(I)由三视图可知三棱柱A1B1C1-ABC为直三棱柱,底面是等腰直角三角形且∠ACB=90°,连接A1C,设A1C∩AC1=O.连接MO,由题意可知A1O=CO,A1M=B1M,所以MO∥B1C. ∵MO⊂平面AC1M,B1C⊄平面AC1M ∴B1C∥平面AC1M; (II)∵A1C1=B1C1,点M是A1B1的中点 ∴C1M⊥A1B1, ∵平面A1B1C1⊥平面AA1B1B,平面A1B1C1∩平面AA1B1B=A1B1, ∴C1M⊥平面AA1B1B ∵C1M⊂平面AC1M ∴平面AC1M⊥平面AA1B1B. |