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143288.com:三棱锥的解答题(一)

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三棱锥的解答题(一)
1、已知 ?ABC 中 ?ACB ? 90 , SA ? 面 ABC , AD ? SC ,求证: AD ? 面 SBC .

S

D A C B

2、如图,已知空间四边形 ABCD 中, BC ? AC, AD ? BD , E 是 AB 的中点。 求证: (1) AB ? 平面 CDE; (2)平面 CDE ? 平面 ABC E A

B

C

D

3 、如图 P 是 ?ABC 所在平面外一点, PA ? PB, CB ? 平面 PAB , M 是 PC 的中点, N 是 AB 上的点,

AN ? 3 NB (1)求证: MN ? AB ; (2)当 ?APB ? 90 , AB ? 2 BC ? 4 时,求 MN 的长。

P M

C

A N

B

4、已知四边形 ABCD 是空间四边形, E , F , G, H 分别是边 AB, BC, CD, DA 的中点 (1) 求证:EFGH 是平行四边形 (2) 若 BD= 2 3 ,AC=2,EG=2。求异面直线 AC、BD 所成的角和 EG、BD 所成的角。 A E B F C G H D


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