Chapter 2.1 Notes Conditional Statements – If then form If I am in Geometry class, then I am in my favorite class at IWHS. Hypothesis Conclusion

Original Sentence - Converse – Inverse – Contrapositive -

Postulate 5 – Through any two points there exist exactly one line. Postulate 6 – A line contains at least two points Postulate 7 – If two lines intersect, then their intersection is exactly one point. Postulate 8 – Through any three noncollinear points there exists exactly one plane. Postulate 9 – A plane contains at least three noncollinear points Postulate 10 – If two points line in a plane, then the line containing them lies in the plane. Postulate 11 – If two planes intersect, then their intersection is a line.

Chapter 2.2 Notes Biconditional Statement – if and only if statement I am having fun if and only if I am in Geo. Class. * A true biconditional statement is true both forward and backwards.

Perpendicular Lines – two lines that intersect to form a right angle. Line Perpendicular to a plane – is a line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it.

Chapter 2.3 Notes New way to write Conditional & Biconditional statements ~ - means not - means if-then statement - means if and only if statement Example: Let P = It is lunch time Q = I will go to D.Q. P ~Q ____________________________

Two laws of Deductive Reasoning * Law of Detachment – If p q is a true conditional statement and p is true, then q is true. * Law of Syllogism – If p q and q r is a true conditional statement, then p r is true.

Chapter 2.4 Notes Addition Property – If a = b, then a + c = b + c Subtraction Property - If a = b, then a - c = b – c Multiplication Property - If a = b, then a * c = b * c Division Property - If a = b, then a / c = b / c Reflexive Property - for any real # a, a = a Symmetric Property – if a = b then b = a Transitive Property - if a = b and b = c, then a = c Substitution Property - if b = c, then where I see a b I can substitute in a c

Chapter 2.5 Notes Types of Proofs 1)two-column proofs – has numbered statements and reasons that show the logical order of an argument 2)Paragraph proof – a type of proof written in paragraph form Any time you go from saying AB = CD to AB ~ CD and vise versa it is the (Definiton of Congruence)

Chapter 2.6 Notes Right Angle Congruence Thm – all right angles are congruent Congruent Supplements Thm – If 2 angles are supp. to the same angle then they are congruent. Congruent Complements Thm – If 2 angles are comp. to the same angle then they are congruent.

Linear Pair Postulate – If 2 angles form a linear pair, then they are supplementary. Vertical Angles Thm – Vertical angles are congruent