Transcript Chapter 2.1 Notes - Illini West High School

Chapter 2.1
Common Core G.CO.9, G.CO.10 & G.CO.11 Prove
theorems about lines, angles, triangles and
parallelograms.
Objective – To use inductive reasoning to make
conjectures.
Ch 2.1 Notes
Inductive Reasoning – is reasoning based on
patterns you observe.
Conjecture – is a conclusion you reach using
inductive reasoning.
Counterexample – is an example that shows
that a conjecture is incorrect
Chapter 2.2
Common Core G.CO.9, G.CO.10, & G.CO.11 Prove
theorems about lines, angles, triangles, and
parallelograms.
Objectives – To recognize conditional statements
and their parts. To write converses, inverses, and
contrapositives of conditionals.
Ch 2.2 Notes
Conditional Statements – is an if-then statement
If I am in Geometry class, then I am in my favorite class at IWHS.
Hypothesis
Conclusion
• Original Sentence –
• Converse –
• Inverse –
• Contrapositive -
Chapter 2.3
Common Core Common Core G.CO.9, G.CO.10, &
G.CO.11 Prove theorems about lines, angles,
triangles, and parallelograms.
Objective – To write biconditionals and recognize
good definitions.
Chapter 2.3 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.
New way to write Conditional & Biconditional
statements
~ - means not
- means if-then statement
- means if and only if statement
Chapter 2.4
Common Core GCommon Core G.CO.9, G.CO.10, &
G.CO.11 Prove theorems about lines, angles,
triangles, and parallelograms.
Objective – To use the Law of Detachment and the
Law of Syllogism.
Ch 2.4 Notes
Deductive Reasoning – (sometimes
called logical reasoning) is the
process of reasoning logically form
given statements or facts to a
conclusion.
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 2.5
Common Core GCommon Core G.CO.9, G.CO.10, &
G.CO.11 Prove theorems about lines, angles,
triangles, and parallelograms.
Objective – To connect reasoning in algebra and
geometry.
Ch 2.5 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
*Distributive Property –
a(b+c) =
Proof – is a convincing argument that uses
deductive reasoning. A proof logically shows
why a conjecture is true.
Two-Column Proof – lists each statement on the
left and justifies it with a statement on the right.
Paragraph Proof – is written as sentences in a
paragraph (Ch 2.6)
Chapter 2.6
Common Core G.CO.9 Prove theorems about lines
and angles. Theorems include…vertical angles are
congruent.
Objective – To prove and apply theorems about
angles.
Ch 2.6 Notes
Vertical Angles Thm – Vertical 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.
Right Angle Congruence Thm –
all right angles are congruent
Theorem 2.5 – if two angles are congruent and
supplementary, then each is a right angle.