Geometric Postulates
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- Ruler Postulate
- "The points on a line can be matched one to one with real numbers. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B" ~Ron Larson, Laurie Boswell, Lee Stiff
- Segment Addition Postulate
- "If B is between A and C, then AB+BC=AC. If AB+BC=AC, then B is between A and C." ~Ron Larson, Laurie Boswell, Lee Stiff
- Protractor Postulate
- "Consider a point A on one side of line OB. The rays of the line OA can be amtched one to one with the real numbers from 0 to 180. The measure of angle AOB is equal to the absolute value of the different between the real numbers for Ray OA and Ray OB"~Ron Larson, Laurie Boswell, Lee Stiff
- Angle Addition Postulate
- "If P is in the interior of angle RST then the measure of angle RSP + the emasure of angle PST = the measure of angle RST"~Ron Larson, Laurie Boswell, Lee Stiff
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- "Through any two points there exsists exactly one line"~Ron Larson, Laurie Boswell, Lee Stiff
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- "A line contains at least two points"~Ron Larson, Laurie Boswell, Lee Stiff
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- "If two lines intersect, then their intersection is exactly one point"~Ron Larson, Laurie Boswell, Lee Stiff
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- "Through any three noncollinear points there exsists exactly one plane"~Ron Larson, Laurie Boswell, Lee Stiff
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- "A plane contains at least three noncollinear points."~Ron Larson, Laurie Boswell, Lee Stiff
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- "If two points lie in a plane, then the line containing them lies in the plane"~Ron Larson, Laurie Boswell, Lee Stiff
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- "If two planes intersect, then their intersection is a line"~Ron Larson, Laurie Boswell, Lee Stiff
- Linear Pair Postulate
- "If two angles form a linear pair, then they are supplementary"~Ron Larson, Laurie Boswell, Lee Stiff
- Parallel Postulate
- "If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line"~Ron Larson, Laurie Boswell, Lee Stiff
- Perpendicular Postulate
- "If there is a line and a point not on the line, then there is exactly one line through the pint perpendicular to the given line"~Ron Larson, Laurie Boswell, Lee Stiff
- Corresponding Angles Postulate
- "if two parallel lines are cut by a tranversal, then the pair of corresponding angles are congruent"~Ron Larson, Laurie Boswell, Lee Stiff
- Corresponding Angles Converse
- "If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel"~Ron Larson, Laurie Boswell, Lee Stiff
- Slopes of Parallel Lines
- "In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope"~Ron Larson, Laurie Boswell, Lee Stiff
- Slopes Of Perpendicular lines
- "In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular"~Ron Larson, Laurie Boswell, Lee Stiff
- Side-Side-Side (SSS) congruence Postulate
- "If three sides of a triangle are congruent to three sides of a second triangle, then the two triangles are congruent"~Ron Larson, Laurie Boswell, Lee Stiff
- Side-Angle-Side (SAS) Congruence Postulate
- "If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent"~Ron Larson, Laurie Boswell, Lee Stiff
- Angle-Side-Angle (ASA) Congurence Postulate
- "If two angles and the included side of one triangle are congruent to the two angles and the included side of a second triangle, then the two triangles are congreunt"~Ron Larson, Laurie Boswell, Lee Stiff
- Area of a Square Postulate
- "The area of a square is the square of the length of its side.."~Ron Larson, Laurie Boswell, Lee Stiff
- Area Congruence Postulate
- "If two polygons are congruent, then they have the same area"~Ron Larson, Laurie Boswell, Lee Stiff
- Area Addition Postulate
- "The area of a region is the sum of the areas of its nonoverlapping parts"~Ron Larson, Laurie Boswell, Lee Stiff
- Angle-Angle (AA) Similarity Postulate
- "If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar"~Ron Larson, Laurie Boswell, Lee Stiff
- Arc Addition Postulate
- "The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs"~Ron Larson, Laurie Boswell, Lee Stiff
- Volume of a Cube
- "The volume of a cube is the cube of the length of its side"~Ron Larson, Laurie Boswell, Lee Stiff
- Volume Congruence Postulate
- "If two polyhedra are congruent thent hey have the same volume"~Ron Larson, Laurie Boswell, Lee Stiff
- Volume Addition Postulate
- "The volume of a solid is the sum of the volumes of all its nonoverlapping parts"~Ron Larson, Laurie Boswell, Lee Stiff