Tuesday, January 27, 2009

Elearn Geometry Problem 235: Parallelogram, Transversal line, Perpendicular lines

Problem: Parallelogram, Transversal line, Perpendicular lines

See complete Problem 235 at:
gogeometry.com/problem/p235_parallelogram_transversal_perpendicular_lines.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

2 comments:

  1. draw AB" // A'C', B" is point BB' meet it
    draw DD" // A'C', D" is point DD' meet it

    tr ABB" and DCD" are similar ( equal ang between side and perpend)

    b+a / AB = c+d / CD
    or b+a = c+d

    ReplyDelete
  2. See the drawing

    - A’D’ is the projection of AD on A’C’ and B’C’ if the projection of BC on the same A’C’
    - AD=BC=>A’D’=B’C’
    - Draw a parallel of AD passing through A’ intersecting DD’ in L
    - AA’=D’L=a => D’L=d-a
    - Draw a parallel of BC passing through C’ intersecting BB’ in K
    - CC’=BK=c => B’K=b-c
    - ΔA’D’L is congruent to Δ C’B’K => D’L=B’K
    - => d-a=b-c
    - Therefore d+c=a+b

    ReplyDelete