6. We end this introduction to the Analytic Foundations to Geometry with "Corresponding parts of congurent triangles are congruent" because this is such a major technique in a synthetic development of geometry that an analytic foundation should get to this point. A triangle has six parts: three angles and three sides. The congruent triangle criteria state that if a certain three parts in one triangle are congruent to the corresponding three parts in another triangle, then the triangles are congruent, and if the triangles are congruent, then all of their corresponding parts, including the three parts which we did not notice were congruent to begin with, will also be congruent. This is a major technique for getting more information. When using "Corresponding parts of congurent triangles are congruent" as a reason in a synthetic proof, especially a two column proof, it is often abbreviated to "CPCTAC", or more simply, "CPCTC". Note all that is involved in getting here.

Return to text

Analytic Foundations of Geometry

Robert S. Wilson