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."

"If there is a problem you can't solve, then there is an easier problem you can't solve: find it." George Polya.

"My method to overcome a difficulty is to go round it." George Polya.

"Solving problems is a practical art, like swimming, or skiing, or playing the piano: You can learn it only by imitation and practice." George Polya.

"An idea which can be used once is a trick. If it can be used more than once it becomes a method." George Polya and Gabor Szego.

"Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper." George Polya.

"The apex and culmination of modern mathematics is a theorem so perfectly general that no particular application of it is feasible." George Polya.

"The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them." George Polya.

"A Great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery." George Polya.