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Learn about the basic principles in geometry, including postulates, theorems, and paragraph proofs. Understand key concepts like lines, points, and planes, and how to construct logical arguments for proofs. Practice applying the Midpoint Theorem and mastering the elements of a good proof.
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Postulates and Paragraph Proofs Section 2-5
postulate or axiom – a statement that describes a fundamental relationship between the basic terms of geometry. Postulates are accepted as true. • proof – a logical argument in which each statement you make is supported by a statement that is accepted as true. • theorem – a statement or conjecture that has shown to be true.
Postulates • 2.3 A line contains at least 2 points. • 2.4 A plane contains at least 3 points not on the same line. • 2.5 If 2 points lie in a plane, then the entire line containing those points lies in that plane.
2.6 If 2 lines intersect, then their intersection is exactly one point. • 2.7 If 2 planes intersect, then their intersection is a line.
Midpoint Theorem (2.8) • If M is the midpoint of , then B M A
5 Parts of Good Proof • State theorem or conjecture to be proved. • List the given information. • Draw a diagram if possible. • State what is to be proved. • Develop a system of deductive reasoning.
