Conjectures are hypotheses or educated guesses about general rules of mathematics. They are generalizations based on observations of multiple specific cases.

Every day in our lives, we make conjectures. It’s all about seeing patterns and then concluding that the patterns will continue.

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For example, in geometry, something you could well conjecture about is when you construct several triangles and find out about the measures of the three angles. You may conjecture that the measures of the three angles of a triangle sum up to 180 degrees.

Well, your conjecture could well be true. Actually, it has been proven to be true. Now, that’s exactly what a theorem is.

Theorems are conjectures that have been proven by using mathematical reasoning. These are actually theorems.

The theorem is that the sum of all measures of a triangle’s angles is 180 degrees. This is true with all triangles. The three angles, when added together, will at all times be 180 degrees.