See complete Problem 237 at:

gogeometry.com/problem/p237_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 237: 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 237: Square, Midpoints, Exterior Line...":Let H' and F' be the projections of H and F on the exterior line. We obtain the trapezoids HH'F'F, AA'D'D and BB'C'C. In this trapezoids we have :

m = (HH'+FF')/2;

HH'=(AA'+DD')/2=(a+d)/2

FF'=(BB'+CC')/2=(b+c)/2

From this relations results :

m=(a+b+c+d)/4 that it mean :

4m=a+b+c+d.