Geometry Problems, Online Education
Online Geometry Problem 876: Equilateral Triangle, any Point, Perpendicular, Right Triangle Area, Sum of Areas. Level: High School, College, Mathematics Education

The figure below shows an equilateral triangle ABC of area S. P is any point and PD, PE, and PF are perpendicular to AB, BC, and AC, respectively. If S1, S2, S3, S4, S5, and S6 are the areas of the shaded regions, prove that S1+S3+S5 = S2+S4+S6 = S/2. This entry contributed by Ajit Athle.

 

Geometry problem 876: Equilateral Triangle, any Point, Perpendicular, Right Triangle Area, Sum of Areas
 


 

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given." 

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