Proving Geometry Statements of Constructive Type

This paper presents a method to generate non-degenerate conditions in geometric form for a class of geometry statements of constructive type, called Class C. We prove a mathematical theorem that in the irreducible case, the non-degenerate conditions generated by our method are sufficient for a geometry statement in Class C to be valid in metric geometry. About 400 among 600 theorems proved by our computer program are in Class C.