See complete Problem 151
Quadrilateral, Area, Trisection of Sides. Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
Sunday, July 27, 2008
Elearn Geometry Problem 151
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proved from Proposed Problem 150, EFMN=S/3=PQGH, so S1+S3=S2+S4
ReplyDeletebu çözümü anlamadık daha açıklayıcı olabilir misiniz yorumları olan yokmu acil çok
ReplyDeleteA more "explicit" solution to problem 151.
ReplyDeleteLet S5 be the area of the central quadrilateral. As proved in problem 150,
S(GHPQ) = S/3 and S(EFMN) = S/3.
Then S(GHPQ) = S1 + S3 + S5 = S/3 and
S(EFMN) = S2 + S4 + S5.
Hence S1 + S3 = S2 + S4 = S/3 – S5.
Solution posted on Twitter:
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https://twitter.com/panlepan/status/894134252383719424
Your solution on Twitter has been embedded at http://www.gogeometry.com/problem/p151_quadrilateral_area_trisection.htm
DeleteThanks Vincent
Los escaques están en una doble progresión aritmética, por lo que los simétricamente dispuestos suman 2/n^2 y el central, si lo hay, 1/n^2.
ReplyDeleteApplet de #GeoGebra: http://bit.ly/2JuTtNe
Twitter: https://twitter.com/ilarrosac/status/1005973237505937409