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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## 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.

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Post Comments (Atom)

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.