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 Proofs1) 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 NotesRight 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