Tuesday, January 13, 2009

Elearn Geometry Problem 223: Viviani Theorem, Isosceles Triangle

Altitude, Distance
In an isosceles triangle ABC (AB = BC), the sum of the distances from any point on AC to the equal sides is equal to the altitude of the equal sides.


 Geometry Problem 223. Viviani Theorem
See complete Problem 223 at:
gogeometry.com/problem/p223_viviani_theorem_isosceles_triangle.htm

Level: High School, SAT Prep, College geometry

3 comments:

  1. Area of ABC = Area of ABD + Area of ACD. So :
    AH*BC/2= DF*AB/2 + DE*BC/2.Because AB=BC, we have :
    h*AB/2=f*AB/2 + e*AB/2, from where it results that :
    h=e+f

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  2. tr DEC similar to AHC

    => AC/DC = h/e (1)

    tr DEC similar to AFD

    => (AC-DC)/DC = f/e => AC/DC = (f+e)/e (2)

    from (1) and (2)

    h/e = (f+e)/e => h = f+e

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