Sunday, January 25, 2009

Elearn Geometry Problem 233: Parallelogram, Exterior line, Perpendicular lines

Problem: Parallelogram, Exterior line, Perpendicular lines

See complete Problem 232 at:
gogeometry.com/problem/p233_parallelogram_perpendicular_lines.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

3 comments:

  1. Let be O the intersection of AC and BD, and O' the projection of O on the exterior line. Let denote by o the lenght of OO'.
    In the trapezoid BB'D'D :
    o=(b+d)/2
    In the trapezoid AA'C'C :
    o=(a+c)/2.
    From this relations we have that :
    a+c=b+d

    ReplyDelete
  2. like P234, 235

    draw AB", DC" // A'C'

    b-a /AB = c-d/CD
    b-a = c-d => b+d = c+a

    ReplyDelete
  3. Draw D'D''DD''' parallel to A'B'D'C' thro' D.
    where D',D'',D''' lie on AA', BB', CC' resp.
    now, D'A' = D''B' = DD' = D'''C'.
    so, it requires us to prove that AD' + CD''' = BD'' which comes from problem 232.

    ReplyDelete