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Math Postulates
| Term | Definition |
|---|---|
| The Two Line Postulate | The intersection of two lines is a point |
| The Two Plane Postulate | The intersection of two planes is a line |
| The Two Point Postulate | Through any two points there is one and only one line |
| The Three Noncollinear Points Postulate | Through any three noncollinear points there is one and only one plane |
| The Two Points Plane Postulate | If two points are in a plane, then the line containing them is in the plane |
| Segment Congruence Postulate | If two segments have the same length as measured by a fair ruler, then the segments are congruent. Also, If two segments are congruent, then they have the same length as measured by a fair ruler |
| Segment Addition Postulate | If point R is between points P and Q on a line, then PR + RQ = PQ |
| Angle Addition Postulate | If point S is in the interior in <PQR then m<PQS + m<SQR = m<PQR |
| Angle Congruence Postulate | If angles have the same measure, then they are congruent. If two angles are congruent, then they have the same measure. |
| Linear Pair Property | If two angles form a linear pair, then they are supplementary |
| If-Then Transitive Property | Given: "If A, then B, then C." You can conclude: "If A, then C." |
| Definition of Adjacent Angles | Adjacent angles are angles in a plane that have their vertices and one side in common but that do not overlap |
| Overlapping Segments Theorem | Given a segment with points A, B, C, and D arranged as shown, the following statements are true. 1) If AB = CD, then AC= BD 2) If AC = BD, then AB = CD |
| Overlapping Angles Theorem | Given <AVD with points B and C in its interior as shown, the following statements are true: 1) If m<AVB = m<CVD, then m<AVC = m<BVD 2) If m<AVC = m<BVD, then m<AVB = m<CVD |
| Valid Form: Modus Ponens | If p then q, p, Therefore, q |
| Valid Form: Modus Tollens | If p then q, Not q, Therefore, not p |
| Invalid Form: Affirming the Consequent | If p then q, q, Therefore, p |
| Invalid Form: Denying the Antecedent | If p then q, Not p, Therefore, not q |
| Summary of the Conditionals | Conditional: If p then q Converse: If q then p Inverse: If ~p then ~q Contrapositive: If ~q then ~p |
| Vertical Angles Theorem | If two angles form a pair of vertical angles, then they are congruent |
| Two Parallel Lines Theorem | Reflection across two parallel lines is equivalent to a translation of twice the distance between the lines and in a direction perpendicular to the lines |
| Two Intersecting Lines Theorem | Reflection across two intersecting lines is equivalent to a rotation about the point of intersection through twice the measure of the angle between the lines |
| Proof by Contradiction | To prove a statement is true, assume it is false and show that this leads to a contradiction |
| Reflectional Symmetry | A figure has reflectional symmetry if and only if its reflected image across a line coincides with the preimage. The line is called an axis of symmetry |
| Rotational Symmetry | A figure has rotational symmetry if and only if it has at least one rotation image, not counting rotation images of 0 degrees of multiples of 360 degrees, that coincides with the original image |
Created by:
LucasPOPO123
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