1. 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