Geometry chapter 3: Postulates, theorems and properties
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27 terms
Terms | Definitions |
|---|---|
 Unique measure assumption | Every angle has a unique measure from 0° to 180° |
| Unique angle assumption | Given any ray BC and a real number r between 0 and 180, there is a unique angle ABC on each side of BC such that m∠ABC = r |
| Straight angle assumption | If BA and BC are opposite rays, then m∠ABC = 180° |
| Zero angle assumption | If AB and AC are the same ray, then m∠ABC = 0° |
| Angle addition Assumption | If angles CBD and CBA are adjacent angles, then m∠CBD + m∠DBA = m∠ABC |
| Equal angle measures Theorem | If two angles have the same measure, their complements have the same measure. If two angles have the same measure, their supplements have the same measure. |
| Linear pair theorem | If two angles form a linear pair, then they are supplementary |
| Vertical angles theorem | If two angles are vertical angles, then their measures are equal |
| Reflexive property of equality | a = a |
| Symmetric property of equality | if a = b, then b = a |
| Transitive property of equality | if a = b, and b = c, then a = c |
| Addition property of equality | If a = b, then a + c = b + c |
| Multiplication property of equality | If a = b, then ac = bc |
| Transitive property of inequality | if a < b and b < c, then a < c |
| Addition property of inequality | If a < b, then a + c < b + c |
| Multiplication property of inequality | If a < b and c > 0, then ac < bc. If a < b and c < 0, then ac > bc |
| Equation to inequality property | If a and b are positive numbers and a + b = c, then c > a and c > b |
| Substitution property | If a = b, the a may be substituted for b in any expression |
| Corresponding angles postulate | If two corresponding angles have the same measure, then the lines are parallel. If the lines are parallel, then corresponding angles have the same measure. |
| Parallel lines and slopes theorem | Two nonvertical lines are parallel if and only if they have the same slope |
| Transitivity of parallelism theorem | If line l is parallel to line m and lin m is parallel to line n, then line l is parallel to line n |
| Sk Theorem 1: size property | Under a size change Sk, the line through any two preimage points is parallel to the line through their images |
| Sk Theorem 2: Collinearity is preserved | Under Sk, the images of collinear points are collinear |
| Sk Theorem 3: Angle measure is preserved | Under Sk, an angle and its image have the same measure |
| Two perpendiculars theorem | If two coplanar lines l and m are each perpendicular to the same line, then they are parallel to each other |
| Perpendicular to parallels theorem | In a plane, if a line is perpendicular to one of the two parallel lines, then it is also perpendicular to the other |
| Perpendicular lines and slopes theorem | Two nonvertical lines are perpendicular if and only if the product of their slopes is -1 |
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