Friday, January 23, 2009

Elearn Geometry Problem 231: Triangle, Midpoint, Transversal

Triangle, Midpoints, Transversal

See complete Problem 231 at:
gogeometry.com/problem/p231_triangle_midpoint_transversal_perpendicular.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

3 comments:

  1. join F and D than FD = CE ( middle line ) (1)

    draw DF" // t than F'F" = d

    Tr DFF" and ECC' are similar ( DF // CE )
    than
    f+d / FD = c / CE from (1)

    f+d = c

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  2. There are two solutions, depending whether D is above D’ or not
    See the drawing

    - Define A’ in D’C’ such as AA’ ⊥ D’C’ and B’ such as BB’’ ⊥ D’C’
    1) Let suppose D above D’ : b > a
    - 2f=a+c
    - d=|b-a|/2
    - b=c
    - d+f=|b-a|/2+(a+c)/2
    - 2(d+f)=b-a+a+c=2c
    - =>c=f+d

    2) Let suppose D under D’ : b < a
    - 2f=a+c
    - d=|b-a|/2
    - b=c
    - d-f=|b-a|/2-(a+c)/2
    - 2(d-f)=-b+a-a-c=-2c
    - =>c=f-d

    ReplyDelete
  3. Complete rectangle FF'C'X

    Tr.s DD'E and FCX are congruent SAS

    So CX = d and so c = d + f

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete