Math Postulates
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| The Two Line Postulate | The intersection of two lines is a point
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| The Two Plane Postulate | The intersection of two planes is a line
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| The Two Point Postulate | Through any two points there is one and only one line
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| The Three Noncollinear Points Postulate | Through any three noncollinear points there is one and only one plane
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| The Two Points Plane Postulate | If two points are in a plane, then the line containing them is in the plane
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| 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
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| Segment Addition Postulate | If point R is between points P and Q on a line, then PR + RQ = PQ
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| Angle Addition Postulate | If point S is in the interior in <PQR then m<PQS + m<SQR = m<PQR
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| Angle Congruence Postulate | If angles have the same measure, then they are congruent. If two angles are congruent, then they have the same measure.
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| Linear Pair Property | If two angles form a linear pair, then they are supplementary
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| If-Then Transitive Property | Given: "If A, then B, then C." You can conclude: "If A, then C."
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| 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
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| 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
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| 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
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| Valid Form: Modus Ponens | If p then q,
p,
Therefore, q
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| Valid Form: Modus Tollens | If p then q,
Not q,
Therefore, not p
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| Invalid Form: Affirming the Consequent | If p then q,
q,
Therefore, p
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| Invalid Form: Denying the Antecedent | If p then q,
Not p,
Therefore, not q
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| Summary of the Conditionals | Conditional: If p then q
Converse: If q then p
Inverse: If ~p then ~q
Contrapositive: If ~q then ~p
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| Vertical Angles Theorem | If two angles form a pair of vertical angles, then they are congruent
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| 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
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| 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
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| Proof by Contradiction | To prove a statement is true, assume it is false and show that this leads to a contradiction
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| 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
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| 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
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