Conjecture and Theorem
Conjecture can be best defined as a hypothesis about a mathematical rule. It is usually created after having witnessed a certain outcome in multiple specific cases. After countless trials are taken to see the validity of a conjecture, if it is proven to be true, it becomes a theorem. A theorem is defined as a conjecture that is proven to be true due to mathematical reasoning.
A conjecture is a hypothesis or educated guess about a general rule of mathematics. It’s a generalization based on observation of multiple specific cases. We all make conjectures every day in life. It’s about seeing a pattern and then concluding that that pattern will continue.
Something you might conjecture about in geometry is if you constructed several triangles and found the measures of the angles, you might conjecture that the sum of the measures of the angles of a triangle is 180 degrees. That conjecture would be true, and has been proven true. That’s what a theorem is. A theorem is a conjecture that has been proven using mathematical reasoning.
This is actually a theorem that the sum of the measures of the angles of a triangle is 180 degrees. That’s true with every triangle. The three angles, when you add them together, will always be 180 degrees.