What is a converse of a theorem that is an thin statement
A converse of a theorem is a statement that has the same logical structure as the original theorem but with the hypothesis and conclusion exchanged.
If a theorem is a thin statement, it means that the hypothesis/condition is not present or is very minimal. In this case, the converse of such a theorem would also be a thin statement, with a minimal or no hypothesis/condition.
For example, if the original theorem is "If a triangle has three congruent sides, then it is equilateral," the converse of this statement would be "If a triangle is equilateral, then it has three congruent sides." Both statements are thin because they have very minimal conditions.
It's important to note that the converse of a theorem is not always true, even if the original theorem is true. In the example given, the original theorem is true, but the converse is not necessarily true because a triangle can have three congruent sides without being equilateral (for example, an isosceles triangle).