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.

## Friday, September 12, 2008

### Elearn Geometry Problem 178

Labels:
area,
quadrilateral,
side,
trisection

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Here's a little theorem:

ReplyDeleteLines 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

iyi günler,

ReplyDeleteçözümde geçen bazı harfler şekil üzerinde olmadığı için çözümü anlayamıyorum. mümkünse soruları yanıtlarken gerekli çizimleri ve harflendirmeleri yapabilir misiniz?

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