Reasoning and Proofs Deductive Reasoning Conditional Statement How do you form logical arguments? How do you prove characteristics of angles and lines? Inductive Reasoning Segment Addition Postulate: If B is between A and C, then AB + BC = AC Conjecture: Unproven Statement that is based on observations. Counter example: A specific case for which a conjecture is false. Angle Addition Postulate: If P is in the interior of RST, then the measure of RST is equal to the sum of the measure of RSP and PST. Right angle congruence theorem: All right angles are congruent. Deductive Reasoning Congruent supplements theorem If two angles are supplementary to the same angle, then they are congruent. Law of Detachment: If the hypothesis of a true conditional statement is true, then the conclusions is also true. Law of Syllogism: If p then q If p and then r If q then r Congruent complements theorem If two angles are complementary to the same angle, then they are congruent. Linear pair postulate: If two angles form a linear pair, then they are supplementary. Conditional Statement Vertical angles congruence theorem: Vertical angles are congruent. Conditional statement: If p then q. Converse: If q then p. Inverse: If NOT p then NOT q. Contrapositive: If NOT q then NOT p. Lines perpendicular to a transversal theorem: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. Perpendicular transversal theorem: If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. Biconditional statement: If and only if