Geometry Unit 2 Power Points

Montero 2012

2.1 to 2.3 Notes and ExamplesPatterns, Conditional Statements, and BiConditional Statements

Essential Vocabulary• Biconditional• Conclusion• Conditional• Conjecture• Contrapositive• Converse• Deductive Reasoning

Essential Vocabulary• Hypothesis• Inductive Reasoning• Inverse • Negation• Theorem

Use Your Textbook to Define all these terms

(page 88)

2.1: Patterns and Inductive Reasoning

• Inductive Reasoning is making a decision based on observable patterns

• A Conjecture is a conclusion you reach through reasoning inductively

• Essential Problems from Text: Page 86#7, 21, 31, 33,

• Need Help? Watch this video: http://www.khanacademy.org/math/statistics/v/u12-l1-t3-we1-inductive-reasoning-1

2.2: Conditional Statements

• A Conditional Statement is a statement that has the form “If-Then”

• We say “if p then q” or “p implies q” where p and q represent events or statements

• Symbolically: p q• Venn Diagram

P q

2.2 Conditional Statements (Page 101 and 102)

Stuck? Watch This: http://www.youtube.com/watch?v=utfC7DMKy3g&safe=active

And http://www.youtube.com/watch?v=LJwuqqcXaPE&safe=active

ESSENTIAL QUESTIONS IN THE TEXT: 92# 1-5, 29, 33, 37, 39, 47

2.3 Biconditional Statements

• A biconditional combines pq and qp as p < -- > q (pg 106)“p if and only if q”• Essential Problems from Text: Page 101 # 11,

13 , 15, 17, 19, 21, 23, 25, 27 and Page 104# 49 and 51

Stuck? Watch This: http://www.youtube.com/watch?v=utfC7DMKy3g&safe=activeAnd http://www.youtube.com/watch?v=LJwuqqcXaPE&safe=active

2.4 Deductive Reasoning

• Deductive Reasoning: is the process of reasoning logically from given statements or facts to a conclusing

• Law of Detachment (pg 113)• Law of Syllogism (pg 115)• Page 110 #11, 13, 15, 17 Need Help? Check These out! http://www.youtube.com/watch?v=ZTfVIMPV8KY&safe=activehttp://www.youtube.com/watch?v=PQjpaaLwk58&safe=active http://www.youtube.com/watch?v=WqIgsya0PjM&safe=active

2.5 Reasoning in Algebra & Geometry • Properties of Equality (page 121)• Distributive Property (page 122)• Properties of Congruence (page 122)• Proof: A convinsing argument that uses

deductive reasoning.• Two-Column Proof: is a proof type which lists

statements on the lefts and reasons or justifications on the right.

• Essential Problems: Page 117 #5-8, 29-33

2.6 Proving Angles are Congruent

Methods for proving Angles are Congruent• They are Marked to be congruent (“Given”)• They are Vertical Angles (pg 128)• They are Congruent Supplements (pg 130)• They are Congruent Complements (pg 131)• They are both Right Angles• They are Congruent and a Linear PairPage 124 #7,13,15, 17, 19, 25