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
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macsim gabriel florin has left a new comment on your post "Elearn Geometry Problem 237: Square, Midpoints, Exterior Line...":
ReplyDeleteLet 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.