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Transcript
Postulates, Definitions, Properties and Theorems Points, Lines and Planes Through any two points there is exactly one line Two Point-One Line Postulate Through any three noncollinear points, there is exactly one plane Three Line-One Plane Postulate A line contains at least two points Minimum Points to a Line Postulate A plane contains at least three noncollinear points Minimum Points to a Plane Postulate If two points lie in a plane, then the entire line containing those points lies in the same plane Point in a Line in a Plane Postulate If two lines intersect, then their intersection is exactly one point Intersecting Lines Postulate If two planes intersect, then their intersection is exactly one line. Intersecting Planes Postulate If M is the midpoint of AB , then AM MB Definition of a Midpoint Two lines are perpendicular if they intersect at right angles Definition of Perpendicular Lines Algebra If a b , then a c b c Addition Property of Equality If a b , then a c b c Subtraction Property of Equality If a b , then a c b c Multiplication Property of Equality If a b , then a b c c If a b , then a can be replaced by b in any equation or expression a a, AB AB, or 1 1 Division Property of Equality Substitution Property Reflexive Property If a b , then b a If AB CD , then CD AB If 1 2 , then 2 1 Symmetric Property If a b and b c , then a c If AB CD and CD EF , then AB EF If 1 2 and 2 3 , then 1 3 Transitive Property Geometry If point B is between points A and C, then AB BC AC Segment Addition Postulate If AZB and BZC are adjacent angles, then mAZB mBZC mAZC Angle Addition Postulate If AB BC , then AB = BC Definition of Congruent Segments If ABC XYZ , then mABC mXYZ Definition of Congruent Angles If two angles form a linear pair, then they are supplementary Supplement Theorem If two angles form a right angle, then they are complementary Complement Theorem Angles that are supplements to the same angle (or congruent angles) are congruent Congruent Supplements Theorem Angles that are complements to the same angle (or congruent angles) are congruent Congruent Complements Theorem If two angles are vertical, then they are congruent Vertical Angles Theorem If two parallel lines are cut by a transversal then corresponding angles are congruent. Corresponding Angles Postulate If two parallel lines are cut by a transversal then alternate interior angles are congruent. Alternate Interior Angle Theorem If two parallel lines are cut by a transversal then alternate exterior angles are congruent. Alternate Exterior Angle Theorem If two parallel lines are cut by a transversal then same side interior angles are supplementary. Same Side Interior Angle Theorem If two parallel lines are cut by a transversal then same side exterior angles are supplementary. Same Side Exterior Angle Theorem
