Home Geometry Problems All Problems 331-340 View or post a solution 
Problem 340. Triangle, Angle Bisectors, Perpendiculars, Exterior Point, Distances. Level: High School, College, SAT Prep.

The figure shows a triangle ABC with the angle bisectors AD and CE. F is a point on the extension of DE and FG, FH, and FM are perpendiculars to AB, BC and AC, respectively. Prove that FH - FG = FM. 

Triangle, Angle bisectors, Distances



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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