See complete Problem 88
Triangle and Quadrilateral Areas, Midpoints. Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
Monday, May 19, 2008
Geometry Problem 88
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See complete Problem 88
Triangle and Quadrilateral Areas, Midpoints. Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
AECN =? DEBM
ReplyDeleteAMB*+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 )
Solution to problem 88. Looking at quadrilateral ABCD, as it was proved in problem 87, quadrilaterals BCNA and BCDM have the same area. So
ReplyDeleteS1 = S(AECN) = S(BCNA) + S(BEC) =
= S(BCDM) + S(BEC) = S(DEBM) = S2.