如图,四棱锥S-ABCD的底面是矩形,SA⊥底面ABCD,P是BC边的中点,AD=2,SA=AB=1。 (1)求证:PD⊥平面SAP; ...

作者: tihaiku 人气: - 评论: 0
问题 如图,四棱锥S-ABCD的底面是矩形,SA⊥底面ABCD,P是BC边的中点,AD=2,SA=AB=1。 (1)求证:PD⊥平面SAP; (2)求三棱锥S-APD的体积。
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解析 (1)证明:易知在△APD中,,AD=2,满足勾股定理,故PD⊥AP。SA⊥底面ABCD,则SA⊥PD。PD同时垂直于平面SAP内的两条相交直线,PD⊥平面SAP。 (2)
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