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.

## Sunday, January 25, 2009

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

Labels:
distance,
median,
parallelogram,
perpendicular,
trapezoid

Subscribe to:
Post Comments (Atom)

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'.

ReplyDeleteIn 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

like P234, 235

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

b-a /AB = c-d/CD

b-a = c-d => b+d = c+a

Draw D'D''DD''' parallel to A'B'D'C' thro' D.

ReplyDeletewhere 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.