Monday, May 19, 2008

Geometry Problem 88



See complete Problem 88
Triangle and Quadrilateral Areas, Midpoints. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.
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2 comments:

  1. c .t . e. oJanuary 31, 2010 at 12:03 PM

    AECN =? DEBM

    AMB*+AMN**+MBN***+BCN****+S=MBC*+MNC**+MND***+CND****+S

    AMN**=MNC** ( M midpoint of AC, the same reason for others)
    S is area of BEC ( common for both )

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  2. Nilton LapaApril 28, 2012 at 7:06 AM

    Solution to problem 88. Looking at quadrilateral ABCD, as it was proved in problem 87, quadrilaterals BCNA and BCDM have the same area. So
    S1 = S(AECN) = S(BCNA) + S(BEC) =
    = S(BCDM) + S(BEC) = S(DEBM) = S2.

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