See complete Problem 87
Area of Quadrilateral and Midpoints of Diagonals. Level: High School, SAT Prep, College geometry
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Monday, May 19, 2008
Geometry Problem 87
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S BCNA =? S BCDM
ReplyDeleteABM+BMC+MNC+AMN =? BMC+MNC+CND+MND (AM=MC=>ABM=BMC)
BMC+AMN =? CND+MND
BMC+MNC =? CND+MND ( AM=MC=>MNC=AMN)
BMNC =? MNCD
BMN+BNC =? MND+NDC but BN=ND=>BMN=MND & BNC=NCD
=> BMN+BNC = MND+NDC or
S1 = S2
S3=BMC+MNC but BMC=ABM & MNC=AMN
=> S3 = 1/2 S1
BCNA =? CDAN
ABN+BNC =? AND+NDC but ABN = AND & BNC = NCD (N midpo)
ABN+BNC = AND+NDC
or S1 = 1/2 S