在三棱柱ABC-A1B1C1中，侧面A1ABB1是菱形，侧面BCC1B1是矩形，C1B1⊥AB，求平面C1AB1把棱柱分成两
\u5728\u4e09\u68f1\u67f1ABC-A1B1C1\u4e2d\uff0c\u4fa7\u9762A1ABB1\u662f\u83f1\u5f62\uff0c\u4fa7\u9762BCC1B1\u662f\u77e9\u5f62\uff0cC1B1\u22a5AB\uff0c\u6c42\u5e73\u9762C1AB1\u628a\u68f1\u67f1\u5206\u6210\u4e24\u90e8\u5206\u7684\u89e3\uff1a\u5982\u56fe\uff0c\u5728\u4e09\u68f1\u67f1ABC-A1B1C1\u4e2d\uff0c\u5e73\u9762C1AB1\u628a\u68f1\u67f1\u5206\u6210\u4e24\u90e8\u5206\uff1b\u4e00\u90e8\u5206\u4e3a\u4e09\u68f1\u9525A-A1B1C1\uff0c\u53e6\u4e00\u90e8\u5206\u591a\u9762\u4f53ABB1C1C\uff0c\u5b83\u4eec\u7684\u4f53\u79ef\u5206\u522b\u8bb0\u4e3aV1\uff0cV2\uff1b\u8bbe\u4e09\u68f1\u67f1ABC-A1B1C1\u7684\u4f53\u79ef\u4e3aV\uff0c\u5219V1=13?S\u25b3A1B1C1?h=13V\uff0cV2=V-13V=23V\uff1b\u6240\u4ee5\uff0cV1\uff1aV2=1\uff1a2\uff0e\u6545\u7b54\u6848\u4e3a\uff1a1\uff1a2
\u3000\u30001\u3001\u5728\u4e09\u68f1\u67f1ABC-A1B1C1\u4e2d\u3002
\u3000\u3000\u56e0\u4e3aAB\u22a5BC\uff0c\u6240\u4ee5BC\u22a5\u5e73\u9762A1ABB1\uff0c\u53c8A1B\u5728\u54c1\u9762CA1B\u5185\uff0c\u6240\u4ee5\u9762CA1B\u22a5\u9762A1ABB1
\u3000\u30002\u3001\u75311\u6240\u8bc1A1B\u22a5BC\uff0c\u53c8A1ABB1\u4e3a\u83f1\u5f62\uff0c\u6240\u4ee5A1B=4\uff0c\u7b97\u51faA1C=5\u3002\u5982\u4f60\u56fe\u6240\u4f5c\u865a\u7ebf\uff0c\u4f5cA1D\u22a5B1B\uff0cA1ABB1\u4e3a\u83f1\u5f62\uff0c\u6240\u4ee5A1D=\u6839\u53f7\u4e0b12.\u5728\u76f4\u89d2\u4e09\u89d2\u5f62A1DC\u4e2d \u53ef\u4ee5\u7b97\u51faCD=\u6839\u53f7\u4e0b13\uff0c\u6240\u4ee5\u6b63\u5207\u4e3a\u6839\u53f7\u4e0b12/13.
\u3000\u30003\u3001\u5728\u83f1\u5f62A1ABB1\u4e2d \u8fde\u63a5AB1,\u4ea4\u70b9\u4e3aN\uff0c\u5219\u6709A1B\u22a5AB1\uff0c\u5728\u4e09\u68f1\u67f1ABC-A1B1C1\u4e2d\uff0cBC//B1C1,\u6240\u4ee5B1C1//\u9762A1BC,\u70b9C1\u5230\u5e73\u9762A1CB\u7684\u8ddd\u79bb\u5c31\u662f\u70b9B1\u5230\u5e73\u9762A1CB\u7684\u8ddd\u79bb\uff0c\u5373B1N\u7684\u957f\u5ea6\u3002
\u3000\u3000B1N=\u6839\u53f7\u4e0b12
\u3000\u3000\u89e3\u9898\u601d\u8def\u5c31\u662f\u8fd9\u6837\uff0c\u4f60\u81ea\u5df1\u518d\u9a8c\u8bc1\u4e00\u4e0b\u5427
连接BC1
用等积变化做
V(A-A1B1C1)：V剩余=
V(A-A1B1C1)：V(A-BCC1)+V(A-BB1C1)=V(A-A1B1C1):2V(A-BCC1)
V(A-BCC1)=V(C1-ABC) 高相等
所以V(A-A1B1C1)：V剩余=1:2
1.因为BCC1B1 是矩形，所以BC∥B1C1 ，因为C1B1⊥AB所以CB⊥AB，又因为A1ABB1是菱形
所以C1B1⊥A1B1。.
2.因为A1ABB1是菱形，所以AB=A1B1。因为BCC1B1 是矩形，所以BC=B1C1
终上，三角形ABC=三角形A1B1C1
由于高相等
所以体积相等
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