Download Geometry Unit 2 Power Points

Geometry Unit 2 Power Points
Montero 2012
2.1 to 2.3 Notes and Examples
Patterns, 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-t3we1-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)
ESSENTIAL QUESTIONS IN THE TEXT: 92# 1-5, 29, 33, 37, 39, 47
Stuck? Watch This:
http://www.youtube.com/watch?v=utfC7DMKy3g&safe=active
And
http://www.youtube.com/watch?v=LJwuqqcXaPE&safe=active
2.3 Biconditional Statements
• A biconditional combines pq and qp 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=active
And 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=active
http://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 Pair
Page 124 #7,13,15, 17, 19, 25