Saturday, January 31, 2009

Elearn Geometry Problem 236: Quadrilateral, Midpoints, Exterior line, Perpendicular lines

Problem: Quadrilateral, Midpoints, Exterior line, Perpendicular lines

See complete Problem 236 at:
gogeometry.com/problem/p236_quadrilateral_midpoint_exterior_line_perpendicular.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

2 comments:

  1. macsim gabriel florin has left a new comment on your post "Elearn Geometry Problem 236: Quadrilateral, Midpoints...":

    Let A' , B', C' and D' the projections of A, B, C, D on the exterior line.We obtain the trapeziods AA'B'B, BB'C'C, CC'D'D, DD'A'A. In this trpezoids we have :
    e=(AA'+BB')/2
    f=(BB'+CC')/2
    g=(CC'+DD')/2
    h=(DD'+AA')/2
    From this relations results that e+g=f+h

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  2. See the drawing

    - From problem 146, EH//FG => E’H’=F’G’
    - Draw E’’H’//EH, E’’ on EE’ =>E’E’’=e-h
    - Draw F’’G’//FG, F’’ on FF’ => F’F’’=f-g
    - E’’H’//EH, F’’G’//FG and EH//FG => E’’H’//F’’G’
    - =>E’’E’H’ is similar to F’’F’G’
    - E’H’=F’G’ => E’’E’H’ is congruent to F’’F’G’
    - =>E’E’’=F’F’’
    -=>e-h=f-g
    Therefore e+g=f+h

    ReplyDelete