Geometry Problems, Online Education
Online Geometry Problem 867: Isosceles Triangle, Median, Perpendicular, Angle, Congruence. Level: High School, College, Mathematics Education

The figure below shows a triangle ABC with AB = BC and BE perpendicular to median AD. If angle DAC = angle DBE, and DE = 1, find AE.


Geometry problem 867: Isosceles Triangle, Median, Perpendicular, Angle, Congruence


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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