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Online Geometry Problem 882: Triangle, Angle x, 2x, 7x, Cevian, Congruence, Auxiliary Lines. Level: High School, Honors Geometry, College, Mathematics Education

In a triangle ABC, D is on AB so that AD = BC, angle ACD = x, angle A = 2x, and angle BCD = 7x. Find x.


 

Geometry Problem: Triangle, Angle x, 2x, 7x, Cevian, Congruence, Auxiliary Lines


 

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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