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Problems(1)

Intersection of plane with pyramid being a parallelogram

Source:

1/3/2011
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.
geometry3D geometrypyramidparallelogramgeometry unsolved