如图所示的三个图中,上面的是一个长方体截去一个角所得多面体的直观图,它的正视图和侧视图在下面画出( 如图的三个图中,上面的是一个长方体截去一个角所得多面体的直观...

\u5982\u56fe\u6240\u793a\u7684\u4e09\u4e2a\u56fe\u4e2d\uff0c\u4e0a\u9762\u7684\u662f\u4e00\u4e2a\u957f\u65b9\u4f53\u622a\u53bb\u4e00\u4e2a\u89d2\u6240\u5f97\u591a\u9762\u4f53\u7684\u76f4\u89c2\u56fe\uff0c\u5b83\u7684\u6b63\u89c6\u56fe\u548c\u4fa7\u89c6\u56fe\u5728\u4e0b\u9762\u753b\u51fa(

\uff081\uff09\u89c1\u89e3\u6790\uff1b\uff082\uff09\u89c1\u89e3\u6790. \u8bd5\u9898\u5206\u6790\uff1a\uff081\uff09\u6839\u636e\u51e0\u4f55\u4f53\u7684\u7ed3\u6784\u7279\u5f81\u4e0e\u5b83\u7684\u6b63\uff08\u4e3b\uff09\u89c6\u56fe\u548c\u4fa7\uff08\u5de6\uff09\u89c6\u56fe\u53ef\u5f97\u5176\u4fa7\u89c6\u56fe\uff0e\uff082\uff09\u7531\u539f\u9898\u53ef\u5f97\uff1a\u70b9 \u3001 \u5206\u522b\u662f\u6b63\u65b9\u5f62\u7684\u4e2d\u70b9\uff0c\u53d6 \u2032\u4e0e \u7684\u4e2d\u70b9\u5206\u522b\u4e3a \u3001 \uff0c\u6240\u4ee5 \uff0c\u5373\u53ef\u5f97\u5230 \uff0c\u6839\u636e\u7ebf\u9762\u5e73\u884c\u7684\u5224\u65ad\u5b9a\u7406\u53ef\u5f97\u7ebf\u9762\u5e73\u884c\uff0e\u8bd5\u9898\u89e3\u6790\uff1a\uff081\uff09\u5982\u56fe\uff0c\u4fef\u89c6\u56fe \uff082\uff09\u8bc1\u660e\uff1a\u7531\u591a\u9762\u4f53\u7684\u4fa7\uff08\u5de6\uff09\u89c6\u56fe\u53ef\u5f97\uff1a\u70b9 \u3001 \u5206\u522b\u662f\u6b63\u65b9\u5f62\u7684\u4e2d\u70b9\uff0c\u53d6 \u2032\u4e0e \u7684\u4e2d\u70b9\u5206\u522b\u4e3a \u3001 \uff0c\u6240\u4ee5 \uff0c\u6839\u636e\u51e0\u4f55\u4f53\u7684\u7ed3\u6784\u7279\u5f81\u53ef\u5f97\uff1a \uff0c\u6240\u4ee5 \uff0c\u56e0\u4e3a \u5e73\u9762 \uff0c \u5e73\u9762 \u6240\u4ee5 \u5e73\u9762 \uff0e

\uff081\uff09\u5982\u56fe\uff082\uff09\u5b83\u53ef\u4ee5\u770b\u6210\u4e00\u4e2a\u957f\u65b9\u4f53\u622a\u53bb\u4e00\u4e2a\u5c0f\u4e09\u68f1\u9525\uff0c\u8bbe\u957f\u65b9\u4f53\u4f53\u79ef\u4e3aV1\uff0c\u5c0f\u4e09\u68f1\u9525\u7684\u4f53\u79ef\u4e3aV2\uff0c\u5219\u6839\u636e\u56fe\u4e2d\u6240\u7ed9\u6761\u4ef6\u5f97\uff1aV1=6\u00d74\u00d74=96cm3\uff0cV2=13?12?2?2?2=43cm3\uff0c\u2234V=v1-v2=2843cm3\uff083\uff09\u8bc1\u660e\uff1a\u5982\u56fe\uff0c\u5728\u957f\u65b9\u4f53ABCD-A\u2032B\u2032C\u2032D\u2032\u4e2d\uff0c\u8fde\u63a5AD\u2032\uff0c\u5219AD\u2032\u2225BC\u2032\u56e0\u4e3aE\uff0cG\u5206\u522b\u4e3aAA\u2032\uff0cA\u2032D\u2032\u4e2d\u70b9\uff0c\u6240\u4ee5AD\u2032\u2225EG\uff0c\u4ece\u800cEG\u2225BC\u2032\uff0c\u53c8EG?\u5e73\u9762EFG\uff0c\u6240\u4ee5BC\u2032\u2225\u5e73\u9762EFG\uff1b

(1)如图

(2)所求多面体的体积V=V长方体?V三棱锥=4×4×6?
1
3
×(
1
2
×2×2)×2=
284
3
(cm3)

(3)证明:如图,

在长方体ABCD-A′B′C′D′中,连接AD′,则AD′∥BC′
因为E,G分别为AA′,A′D′中点,所以AD′∥EG,从而EG∥BC′,
又EG?平面EFG,所以BC′∥平面EFG;

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