The figure below shows an isosceles triangle
ABC (AB = BC) with a point D on AC. Prove that the circumcircles of
triangles ABD and BDC are congruent.
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."