Students' difficulty with reasoning and justification in the context of proofs in geometry has been well documented. Studies reveal that many of the ideas that students are asked to prove are known to be true, and therefore, the process of such proof is likely to remain meaningless and purposeless. The implication of this claim is that students need to be asked to prove mathematical assertions that are not known to them to be true. This puts an enormous responsibility on teachers. The purpose of this paper is to provide examples of 'non-traditional conjectures' that can be explored in the dynamic geometry environment of computer construction programs.