Two angles are supplementary if the sum of their

This preview shows page 68 - 77 out of 96 pages.

Two angles are supplementary if the sum of their measures is 180 degrees.
Image of page 68

Subscribe to view the full document.

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.
Image of page 69
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.
Image of page 70

Subscribe to view the full document.

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."
Image of page 71
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.
Image of page 72

Subscribe to view the full document.