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Intersection of plane with pyramid being a parallelogram

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January 3, 2011
geometry3D geometrypyramidparallelogramgeometry unsolved

Problem Statement

Let ABCDSABCDS be a pyramid with four faces and with ABCDABCD as a base, and let a plane α\alpha through the vertex AA meet its edges SBSB and SDSD at points MM and NN, respectively. Prove that if the intersection of the plane α\alpha with the pyramid ABCDSABCDS is a parallelogram, then SM⋅SN>BM⋅DNSM \cdot SN > BM \cdot DN.
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