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Geometry Chapter 2 Postulates 5 Theorems 2.1 Properties of Segment Congruence: Segment congruence is reflexive, symmetric, and transitive: Through any two points there exists exactly one line. Reflexive: For any segment AB, AB AB . Symmetric: If AB CD , then CD AB . 6 Transitive: If AB CD and CD EF , then AB EF . A line contains at least two points. 2.2 7 If two lines intersect, then their intersection is exactly one point. Through any three noncollinear points there exists exactly one plane. Properties of Angle Congruence: Angle congruence is reflexive, symmetric, and transitive: Reflexive: For any angle A, A A. Symmetric: If A B, then B A. Transitive: If A B and B C, then A C. 8 9 A plane contains at least three noncollinear points. Right Angles Congruence Theorem: All right angles are congruent. 2.3 Congruent Supplements Theorem: If two angles are supplementary to the same angle (or to congruent angles), then the two angles are congruent. 2.4 If two points lie in a plane, then the line containing them lies in the plane. 10 Congruent Complements Theorem: If two angles are complementary to the same angle (or to congruent angles), then the two angles are congruent. 2.5 11 If two planes intersect, then their intersection is a line. Vertical Angles Congruence Theorem: Vertical angles are congruent. 2.6 Linear Pair Postulate: If two angles form a linear pair, then they are supplementary. 12