Transcript Chapter 2.1 Notes

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
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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
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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
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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