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.

## Saturday, January 31, 2009

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

Labels:
distance,
exterior line,
midpoint,
perpendicular,
quadrilateral,
trapezoid

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ReplyDeletemacsim gabriel florinhas 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

See the

ReplyDeletedrawing- 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