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Theorems and postulates, while both similar in usefulness and content, have some major differences. A theorem defined as a statement, usually of a general nature, that can be proven by appeal to postulates, definitions, algebraic properties, and rules of logic. A corollary is a statement that can be proven by a theorem, so it is like a baby theorem. A postulate is defined as a statement that describes a fundamental relationship between the basic terms of geometry. Postulates are accepted as true without proof. What this means is that a theorem is general and can be proven with other theorems, postulates, or properties. A postulate, on the other hand, is accepted as true because to try to prove it would be very hard, if even possible. For Example: |
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Theorem 3-5 If two lines in a plane are cut by a transversal so that the pair of alternate exterior angles are congruent, then the two lines are parallel. Proof: |
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As you can see, it is easily proven in four easy steps. Try and prove this postulate! If two angles of one triangle are congruent to two angle of another triangles, then the triangles are similar. As you can see, it is a lot more complex than a theorem |
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Given: Angle 1 and angle 2 are supplementary Prove: l is parallel to m |
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Theorems and Postulates |
