在四棱锥P-ABCD中,底面ABCD是边长为a的正方形,E,F分别为PC,BD的中点,侧面PAD垂直于底面ABCD,且PA=PD=(根号2/2)AD.(1)求证:EF//平面PAD; (2)求证:平面PAB垂直于平面PCD.
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![在四棱锥P-ABCD中,底面ABCD是边长为a的正方形,E,F分别为PC,BD的中点,侧面PAD垂直于底面ABCD,且PA=PD=(根号2/2)AD.(1)求证:EF//平面PAD; (2)求证:平面PAB垂直于平面PCD.](/uploads/image/z/8576147-11-7.jpg?t=%E5%9C%A8%E5%9B%9B%E6%A3%B1%E9%94%A5P-ABCD%E4%B8%AD%2C%E5%BA%95%E9%9D%A2ABCD%E6%98%AF%E8%BE%B9%E9%95%BF%E4%B8%BAa%E7%9A%84%E6%AD%A3%E6%96%B9%E5%BD%A2%2CE%2CF%E5%88%86%E5%88%AB%E4%B8%BAPC%2CBD%E7%9A%84%E4%B8%AD%E7%82%B9%2C%E4%BE%A7%E9%9D%A2PAD%E5%9E%82%E7%9B%B4%E4%BA%8E%E5%BA%95%E9%9D%A2ABCD%2C%E4%B8%94PA%3DPD%3D%28%E6%A0%B9%E5%8F%B72%2F2%29AD.%281%29%E6%B1%82%E8%AF%81%EF%BC%9AEF%2F%2F%E5%B9%B3%E9%9D%A2PAD%3B+%282%29%E6%B1%82%E8%AF%81%EF%BC%9A%E5%B9%B3%E9%9D%A2PAB%E5%9E%82%E7%9B%B4%E4%BA%8E%E5%B9%B3%E9%9D%A2PCD.)
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