Term
Point-Line-Plane Postulate
a. Unique line Assumption |
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Definition
[image]
Through any two points, there is exactly one line. |
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Term
Point-Line-Plane Postulate
b. Number line assumption |
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Definition
| Every line is a set of points that can be put into a 1 to 1 correspondence with the real numbers, with any point on it corresponding to 0 and any other point corresponding to 1. |
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Term
Point-Line-Plane Postulate
c. Dimension Assumption |
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Definition
1. Given a line in a plane, there is at least 1 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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Term
Point-Line-Plane Postulate
d. Flat Plane Assumption |
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Definition
| If two points lie in a plane, the line containing them lies in the plane |
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Term
Point-Line-Plane Postulate
e. Unique Plane Assumption |
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Definition
| Through three noncollinear points, there is exactly 1 plane. |
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Term
Point-Line-Plane Postulate
f. Intersecting Plane Assumption |
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Definition
| If two different planes have a point in common, then their intersection is a line. |
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Term
Distance Postulate
a. Uniqueness Property |
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Definition
| On a line, there is a unique distance between two points |
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Term
Distance Postulate
b. Distance Formula |
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Definition
| If the two points on a line have coordinates x and y, the distance between them is [x - y] |
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Term
Distance Postulate
c. Additive Property |
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Definition
| If B is on segment AC, then AB + BC = AC. |
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Term
Triangle Inequality Postulate
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Definition
| The sum of the lengths of any two sides of a triangle is greater than the length of the third side |
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Term
Angle Measure Postulate
a. Unique Measure Assumption |
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Definition
| Every angle has a unique measure from 0 to 180 |
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Term
Angle Measure Postulate
b. Unique Angle Assumption |
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Definition
| Given any ray VA and any real number r between 0 and 180, there is a unique angle BVA in each half-plane of line VA such that the measure of angle BVA = r. |
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Term
Angle Measure Postulate
c. Zero Angle Assumption |
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Definition
| If ray VA and ray VB are the same ray, then the measure of angle AVB = 0. |
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Term
Angle Measure Postulate
d. Straight Angle Assumption |
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Definition
| If VA and VB are opposite rays, then the measure of angle AVB = 180 |
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Term
Angle Measure Postulate
e. Angle Addition Property |
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Definition
| If ray VC (except for point V) is in the interior of angle AVB, then the measure of angle AVC + measure of angle CVB = the measure of angle AVB |
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Term
Postulates of Equality
a. Reflexive Property of Equality
b. Symmetric Property of Equality
d. Transitive Property of Equality |
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Definition
a. a = a (dumb property)
b. If a = b then b = a
c. If a = b and b = c then a = c |
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Term
Point-Line-Plane Postulate
a. Unique line Assumption |
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Definition
| Through any two points, there is exactly one line. |
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Term
| Addition Property of Equality |
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Definition
| If a = b, then a + c = b + c |
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Term
| Multiplication Property of Equality |
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Definition
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Term
Postulate of Inequality
Transitive Property of Inequality |
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Definition
| If a is less than b and b is less than c, then a is less than c. |
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Term
| Addition Property of Inequality |
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Definition
| If a is less than b, then a + c is less than b + c. |
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Term
| Multiplication Properties of Inequality |
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Definition
If a is less than b and c is greater than 0, then ac is less than ab
If a is less than b and c is less than 0, then ac is greater than ab |
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Term
| Postulate of Inequality Property |
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Definition
| If a and b are postive numbers and a + b = c, then c is greater than a and c is greater than b. |
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Term
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Definition
| If a = b, then a may be substituted for b in any expression. |
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Term
Corresponding Angles Postulate
Suppose two coplanar lines are cut by a transversal |
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Definition
a. If two corresponding angles have the same measure, then the lines are parallel.
b. If the lines are parallel, then corresponding angles have the same measure. |
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Term
Reflection Postulate
A-B-C-D postulate |
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Definition
a. Angle measure is preserved.
b. Betweenness is preserved
c. Collinearity is preserved.
d. Distance is preserved.
e. 1 to 1 correspondence
f. Orientation is reversed |
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