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# Two angles are supplementary if the sum of their

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Two angles are supplementary if the sum of their measures is 180 degrees.

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Axioms An axiom is a proposition accepted as true without proof within the mathematical system. There are many examples of axioms in mathematics: Example: In Euclidean geometry the following are axioms Given two distinct points, there is exactly one line that contains them. Given a line and a point not on the line, there is exactly one line through the point which is parallel to the line.
Theorems A theorem is a proposition of the form p q which must be shown to be true by a sequence of logical steps that assume that p is true, and use definitions, axioms and previously proven theorems.

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Lemmas and corollaries A lemma is a small theorem which is used to prove a bigger theorem. A corollary is a theorem that can be proven to be a logical consequence of another theorem. Example from Euclidean geometry: "If the three sides of a triangle have equal length, then its angles also have equal measure."
Types of proof A proof is a logical argument that consists of a series of steps using propositions in such a way that the truth of the theorem is established. Direct proof: p q A direct method of attack that assumes the truth of proposition p, axioms and proven theorems so that the truth of proposition q is obtained.

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