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pGeo C2 Post/The/Cor

pGeometry C2 Postulates/Theorems/Corollaries

TermDefinition
Two Point Postulate Through any two points, there exists exactly one line
Line-Point Postulate A line contains at least two points
Line Intersection Postulate If two lines intersect, then their intersection is exactly one point
Three Point Postulate Though any three noncollinear points, there exists exactly one plane
Plane-Point Postulate A plane contains at least three noncollinear points
Plane-Line Postulate If two points lie in a plane, then the line containing them lies in the plane
Plane Intersection Postulate If two planes intersect, then their intersection is a line
Linear Pair Postulate If two angles form a linear pair, then they are supplementary
Reflexive Property For any segment AB, segment AB is congruent to segment AB. For any angle A, angle A is congruent to angle A.
Symmetric Property If segment AB is congruent to segment CD, the segment CD is congruent to segment AB. If angle A is congruent to angle B, then angle B is congruent to angle A.
Transitive Property If segment AB is congruent to segment CD and segment CD is congruent to segment EF, then segment AB is congruent to segment EF. If angle A is congruent to angle B and angle B is congruent to angle C, then angle A is congruent to angle C.
Right Angles Congruence Theorem All right angles are congruent
Congruent Supplements Theorem If two angles are supplementary to the same angle (or to congruent angles) then they are congruent
Congruent Complements Theorem If two angles are complementary to the same angle (or to congruent angles) then they are congruent
Vertical Angles Congruence Theorem Vertical angles are congruent
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