See complete Problem 87

Area of Quadrilateral and Midpoints of Diagonals. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Monday, May 19, 2008

### Geometry Problem 87

Labels:
area,
diagonal,
midpoint,
quadrilateral

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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