Sunday, January 25, 2009

Elearn Geometry Problem 232: Parallelogram, Vertex, Perpendicular lines

Problem: Parallelogram, Vertex, Perpendicular lines

See complete Problem 232 at:
gogeometry.com/problem/p232_parallelogram_perpendicular_lines.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

3 comments:

  1. Let O be the intersection of AC and BD, and O' the projection of O on the exterior line.
    In the triangle BB'D we have :
    OO'=BB'/2=b/2
    In the trapezoid AA'C'C we have:
    OO'=(AA'+CC')/2=(a+c)/2
    From these relations we obtain b=a+c

    ReplyDelete
  2. draw AB" perpendic to BB'
    tr ABB" and DCC' are similar ( ang B1 = C2 )

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

    ReplyDelete
  3. Let the perpendicular from C to BB' meet BB' at P.
    by AAS congruence, triangle CPB congruent to DA'A.
    hence PB = a.
    now, PB'C'C is a rectangle...
    so, PB' = c.
    Hence b = BB' = BP + PB' = a + c .

    ReplyDelete