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Math Postulates

TermDefinition
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