Friday, September 12, 2008

Elearn Geometry Problem 178

Quadrilateral, Midpoint, Triangles, Area

See complete Problem 178 at:
www.gogeometry.com/problem/p178_quadrilateral_area_trisection_sides.htm

Quadrilateral, Trisection of sides, Area. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

2 comments:

  1. Here's a little theorem:
    Lines L1, L2 and L3 intercept respectively L4, L5 and L6 at A B C, D E F and G H I. If any 2 of the ratios AB:BC, DE:EF and GH:HI, and any 2 of the ratios AD:DG, BE:EH and CF:FI, are the same, then AB:BC=DE:EF=GH:HI and AD:DG=BE:EH=CF:FI.

    Prove:
    construct line L6'//L6 through A,
    DI intercepts L6' at K, by KD:DI=AD:DG=CF:FI, get KC//L5,
    DH intercepts L6' at L, by AL:LK=GH:HI=AB:BC, get LB//KC//L5,
    AD:DG=LD:DH=BE:EH.
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    S_1=[IJKL] with I,J be nearest to A,B
    implying the above theorem, we get QJ=JK=KG and so are the others
    referring to Proposed Problem 150, S_1=[ENMF]/3=S/9

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  2. iyi günler,
    çözümde geçen bazı harfler şekil üzerinde olmadığı için çözümü anlayamıyorum. mümkünse soruları yanıtlarken gerekli çizimleri ve harflendirmeleri yapabilir misiniz?
    teşekkürler

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