5-Con triangles
In geometry, two triangles are said to be 5-Con or almost congruent if they are not congruent triangles but they are similar triangles and share two side lengths (of non-corresponding sides). The 5-Con triangles are important examples for understanding the solution of triangles. Indeed, knowing three angles and two sides (but not their sequence) is not enough to determine a triangle up to congruence. A triangle is said to be 5-Con capable if there is another triangle which is almost congruent to it. The 5-Con triangles have been discussed by Pawley:, and later by Jones and Peterson. They are briefly mentioned by Martin Gardner in his book Mathematical Circus. Another reference is the following exercise Explain how two triangles can have five parts (sides, angles) of one triangle congruent to five parts of the other triangle, but not be congruent triangles. A similar exercise dates back to 1955, and there an earlier reference is mentioned. It is however not possible to date the first occurrence of such standard exercises about triangles. (Wikipedia).
