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Axiom

Geometry Theorems and Postulates for a Midterm

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Geometry
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Distance
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Axiom
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Line segment
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DEFINITIONS?Def. line segment (segment) - part of a line that has 2 definite endpoints?Def. ray - part of a line that starts with a definite endpoint and extends indefinitely in 1 direction?Def. angle - the union of 2 noncollinear rays with a common endpoint?Def. union - elements belonging in 1 or both sets?Def. intersection - elements that belong to both sets?Def. absolute value - |x| = if x _>_ 0; -x if x _<_ 0?Def. segment length - the distance between the endpoints?Def. congruent segments - segments with the same length?Def. midpoint - a point B is called the midpoint of lineAC if A - B - C and AB = BC?Def. segment bisector - a point, line, ray, segment, or plane that passes through the midpoint of a line?Def.

Geometry Theorems and Postulates

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Geometry
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MATH NOTES PART ONE Geometry- A metric system of measuring the earth Four parts of a mathematics system- undefined terms, defined terms, postulates, theorems Defined terms- postulates, theorems Undefined terms- a point (use capitals), a line (name it with capitals, or name it line l), a plane (adds a new dimension) Zero-dimension- the dimension of a point One-dimension- the dimension of a line Two-dimensional- the dimension of a plane Collinear- when two points are on the same line Non-collinear- when two points are NOT on the same line Non-coplanar- if the point can never be in the plane Postulates- statements accepted without proof Theorem- statements that can be proven with postulates Segment- is part of a line that has two endpoints

Geometry

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Geometry ? a Greek term meaning ?measure of the earth? Geometry is concerned with questions of size, shape, and relative positions of figures. The ancient Greek mathematician Euclid applied rigorous logic to the properties of Geometry and created an axiomatic system. Axiom ? self-evident truth that provides a starting point for deductive reasoning; sometimes called a ?postulate? Euclid was so influential that his textbook Elements was taught for over two millennia. What we study is called ?Euclidean Geometry.? There is also non-Euclidean Geometry, which is beyond the scope of this course.
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