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19 Cards in this Set
- Front
- Back
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Distance (AB) |
The between any two points on a coordinatized line is the absolute value of the difference of their coordinates. In symbols the distance between two points with coordinates x and y is |x - y| distance between points A and B is written AB |
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Undefined Terms(in this book) |
Geometric terms: point, line, plane Algebraic and Arithmetic terms: number, equal, set, addition,..... Logical terms: if, then, and, or..... Common English words: the, a, of, in, with,... |
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Point-Line-Plane Assumption |
a. Unique Line Assumption through any two points, there are exactly one line b.Number Line Assumption every line is a set of points that can be put into a one-to-one correspondence with the real numbers, with any point on it corresponding to 0 and any other point corresponding to 1 c.Dimension Assumption (1) Given a line in a plane, there is at least one point in the plane that is not on the line (2) Given a plane in space, there is at least one point in space that is not in the plane |
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Line Intersection Theorem |
Two different lines intersect in at most one point |
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Parallel Lines |
Two coplanar lines m and n are parallel lines, written m // n, if and only if they no points in common or they are identical |
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Line Segment |
The segment (or line segment) with endpoints A and B is the set consisting of the distinct points A and B and all points between A and B |
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Ray |
The ray with endpoint A and containing a second point B consists of the points on segment AB and all points which B is between each of them A |
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Opposite Rays |
ray AB and ray AC are opposite rays if and only if A is between B and C |
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Distance Postulate |
a. Uniqueness Property on a line, there is a unique distance between two points b. Distance Formula if two points on a line have coordinates x and y, the distance between them is |x - y| c. Additive Property if B is on segment AC, then AB + BC= AC |
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Convex Set |
a set in which every segment that connects points of the set lies entirely in the set |
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Instance of a Conditional |
a specific case in which both the antecedent (if part) and the consequent (then part) of the conditional are true |
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Counterexample to a Conditional |
a specific case for which the antecedent (if part) of the conditional is true and its consequent (then part) is false |
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Converse |
The converse of p => q is q => p |
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Midpoint |
The midpoint of segment AB is the point M on segment AB with AM=BM |
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Circle |
A circle is the set of all points in a plane at certain distance, its radius, from a certain point, its center |
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Union of Sets |
set of elements which are in A, in B or in both A and B |
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Intersection of Sets |
set of elements which are in both A and B |
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Polygon |
A polygon is the union of segments in the same plane such that each segment intersects exactly two others, one at each of its endpoints |
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Triangle Inequality Postulate |
The sum of the lengths of any two sides of a triangle is greater than the length of the third side |
