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 illstructured problem. By
“construction,” we mean adding geometric figures (points, lines,
planes) to a problem figure that wasn’t mentioned as "given."
