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 NotesInductive 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• 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

*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.