Geometry Chapter 2.

Slides:

Advertisements

Similar presentations

Chapter 2 Review Lessons 2-1 through 2-6.

Advertisements

Chapter 2 By: Nick Holliday Josh Vincz, James Collins, and Greg “Darth” Rader.

SECTION 2.1 Conditional Statements. Learning Outcomes I will be able to write conditional statements in if- then form. I will be able to label parts of.

Conditional Statements

A conditional is a statement that can be written in the If – Then form. If the team wins the semi-final, then it will play in the championship.

Do Now: 1.Copy Down HW. 2.Describe the pattern, then find the next two numbers in the pattern: 3, 12, 48, 192, …

Section 2.1 Notes Conditional Statements. Conditional Statement A type of logic statement that has two parts: a hypothesis and a conclusion We will write.

CHAPTER 1: Points, Lines, Planes, and Angles

Jeopardy Chapter 2.

2.1 Conditional Statements Goals Recognize a conditional statement Write postulates about points, lines and planes.

10/21/2015Geometry1 Section 2.1 Conditional Statements.

10/21/2015Geometry1 Conditional Statements. 10/21/2015Geometry2 Goals Recognize and analyze a conditional statement Write postulates about points, lines,

2.1 Conditional Statements. Conditional Statement  Conditional statement has two parts, hypothesis and a conclusion.  If _____________, then____________.

Conditional Statements Conditional Statement: “If, then” format. Converse: “Flipping the Logic” –Still “if, then” format, but we switch the hypothesis.

Learning Targets I can recognize conditional statements and their parts. I can write the converse of conditional statements. 6/1/2016Geometry4.

Honors Geometry Chapter 2, Section 1 Inductive Reasoning and Conjecturing.

Ex. 1 Identifying Hypothesis and Conclusion A conditional is an If, then statement Made of two parts Hypothesis and conclusion Hypothesis follows the.

© 2004 Charlean Mullikin All rights reserved

Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement.

 What are conditionals & biconditionals?  How do you write converses, inverses, and contrapositives?

Conditional Statement A conditional statement has two parts, a hypothesis and a conclusion. When conditional statements are written in if-then form, the.

Unit 2 Part 1 Conditional, Converse, Inverse, and Contra- Positive Statements.

Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form.

Section 2-2: Biconditionals and Definitions. Conditional: If two angles have the same measure, then the angles are congruent. Converse: If two angles.

Inductive and Deductive Reasoning. Definitions: Conditionals, Hypothesis, & Conclusions: A conditional statement is a logical statement that has two parts:

Section 2.4 Conditional Statements. The word “logic” comes from the Greek word logikos, which means “reasoning.” We will be studying one basic type of.

2.1 Conditional Statements Goal 1: Recognizing Conditional Statements Goal 2: Using Point, Line, and Plane Postulates CAS 1,3.

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.

Chapter 2 Review Conditional Statements Laws of Logic.

Applied Geometry Lesson 1-4 Conditional Statements & Their Converses Objective: Learn to write statements in if-then form and write the converses of the.

2.1 – Conditional Statements  Conditional Statement  If-Then Form  Hypothesis  Conclusion  Converse  Negation  Inverse  Contrapositive  Equivalent.

Conditional Statements A conditional statement is a statement that can be written in “if-then” form. The hypothesis of the statement is the phrase immediately.

2-3 Laws of Logic The laws of logic can be used to provide a system for reaching logical conclusions. This system is called deductive reasoning. Deductive.

2.1, 2.2 and 5.4: Statements and Reasoning. Conditional is an if-then statement that contains two parts. The part following the if is the Hypothesis.

Reasoning and Proof Chapter – Conditional Statements Conditional statements – If, then form If – hypothesis Then – conclusion Negation of a statement-

Inductive Reasoning Notes 2.1 through 2.4. Definitions Conjecture – An unproven statement based on your observations EXAMPLE: The sum of 2 numbers is.

Reasoning and Proof Chapter Use Inductive Reasoning Conjecture- an unproven statement based on an observation Inductive reasoning- finding a pattern.

Draw a Logical Conclusion:  If you are a lefty then you struggle to use a can opener.  If you like math then you must be smart.  If you are smart then.

Section 2-2 Biconditionals and Definitions. What is a biconditional When both the conditional and converse are true the statement can be written as: If.

Conditional Statements A conditional statement has two parts, the hypothesis and the conclusion. Written in if-then form: If it is Saturday, then it is.

Unit 1-4 If and Then statements Conditional Statements in Geometry.

Chapter 2: Reasoning & Proof Conditionals, Biconditionals, & Deductive Reasoning.

Conditional Statements.  Conditional Statement: A statement that can be written in the form “If p then q.”  Every Conditional Statement has 2 parts:

EXAMPLE 1 Identify a postulate illustrated by a diagram

Geometry Chapter 2 © 2004 Charlean Mullikin All rights reserved

Geometry Chapter 2 © 2004 Charlean Mullikin All rights reserved

Deductive Reasoning, Postulates, and Proofs

2.3 Postulates and Diagrams

2.1 Conditional Statements

2-1 Vocabulary conditional statement hypothesis/conclusion

2-1 Vocabulary conditional statement hypothesis/conclusion

Opener 5. If a number greater than 2 is even, then it’s not prime

UNIT 2 Geometric Reasoning 2.1

Deductive Reasoning.

Inductive and Deductive Reasoning

Y. Davis Geometry Notes Chapter 2.

Lesson 2.1 AIM: Conditional Statements

2.2 Deductive Reasoning Objective:

2.1 Conditional Statements

2.4 Use Postulates and Diagrams

Section 2.1 Conditional Statements

Section 2.1 Conditional Statements

2.1 Conditional Statements

Reasoning and Proofs Deductive Reasoning Conditional Statement

Pearson Unit 1 Topic 2: Reasoning and Proof 2-3: Biconditionals and Definitions Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007.

UNIT 2 Geometric Reasoning 2.1

2.2 If - Then Statements OBJ: (1)To Write Statements in If-Then Form

Conditional Statements

2.4 Conditional Statements

Presentation transcript:

Geometry Chapter 2

Conditionals A conditional is a statement that can be written in the If – Then form. If the team wins the semi-final, then it will play in the championship.

Conditionals The “If” part is called the Hypothesis. If the team wins the semi-final, then it will play in the championship. The “Then” part is called the Conclusion.

Hypothesis  Conclusion Conditionals Hypothesis  Conclusion p  q When If  Then All verbs Then Subject adjectives If are...

If Hypothesis  Then Conclusion Conditionals Conditional If Hypothesis  Then Conclusion p  q Converse If  Then Conclusion Hypothesis Hypothesis Conclusion q  p

Conditionals p  q If the team wins the semi-final, then it will play in the championship. q  p Converse If the team plays in the championship, then it won the semi-final. If it will play in the championship, then the team wins the semi-final.

Conditionals p  q q  p ~ p  ~ q ~ q  ~ p Conditional If the team wins the semi-final, then it will play in the championship. p  q Converse If the team plays in the championship, then it won the semi-final. q  p If the team does not win the semi-final, then it will not play in the championship. Inverse ~ p  ~ q Contrapositive If the team does not play in the championship, then it did not win the semi-final. ~ q  ~ p

True False it could be a lion False it could be a lion True All tigers are cats. Conditional If an animal is a tiger, then it is a cat. True p  q False Converse If an animal is a cat, then it is a tiger. it could be a lion q  p False Inverse If an animal is not a tiger, then it is not a cat. it could be a lion ~ p  ~ q Contrapositive If an animal is not a cat, then it is not a tiger. True ~ q  ~ p

Postulates Through any two points there exists exactly one line. If two points exist, then exactly one line passes through them.

Postulates A line contains at least two points. If a line exists, then it contains at least two points.

Postulates If two lines intersect, then their intersection is exactly one point.

Postulates Through any three noncollinear points there exists exactly one plane. If three noncollinear points exist, then exactly one plane contains them.

Postulates A plane contains at least three noncollinear points. If a plane exists, then it contains at least three noncollinear points.

Postulates If two points lie in a plane, then the line containing them lies in the plane.

Postulates If two planes intersect, then their intersection is a line.

Biconditionals True True p  q q  p p  q Conditional If an angle is acute, then it has a measure less than 90. p  q Converse If an angle has a measure less than 90, then it is an acute angle. True q  p If both the conditional and its Converse are true, then it can Be written as a biconditional. Biconditional p  q “if and only if” An angle is acute if and only if It has a measure less than 90.

Practice http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834817-6&chapter=1&lesson=4

Notice how the original Conditional has been Law of Detachment (1) p  q Notice how the original Conditional has been Broken apart into two pieces. (Detached) (2) p (3) q

Law of Detachment p  q p q If you pass the driving test, then you will get your license. p Brian passed his driving test. q Brian got his license.

(1) p  q (2) q  r (3) p  r Law of Syllogism Notice how all three statements are conditionals with three basic ideas. The repeating part cancels out to give the conclusion. (2) q  r (3) p  r

Law of Syllogism p  q q  r p  r If you pass the driving test, then you will get your license. q  r If you get your license, then you can drive to school. p  r If you pass the driving test, then you can drive to school.

If it is not a conditional and not a p statement, Then there is Working the Laws If it is not a conditional and not a p statement, Then there is NO CONCLUSION! Identify the p and q If no, is it a p? Then check for Detachment. If yes, check for syllogism. Is 2nd statement another conditional ?

3- Joe Nathan has an ID number. Law of Detachment Examples: 1- If a student is enrolled at Lyons High, then the student has an ID number. p  q p: student enrolled @Lyons High q: student has an ID number 2- Joe Nathan is enrolled at Lyons High. p 3- Joe Nathan has an ID number. q Law of Detachment

NO CONCLUSION Examples: 1- If your car needs more power, use Powerpack Motor Oil. p  q p: car needs more power q: use Powerpack Motor Oil q 2- Marcus uses Powerpack Motor Oil. NO CONCLUSION

3- If fossil fuels are burned, then wildlife suffers. Law of Syllogism Examples: 1- If fossil fuels are burned, then acid rain is produced. p  q p: fossil fuels are burned q: acid rain is produced. q  r 2- If acid rain falls, wildlife suffers. 3- If fossil fuels are burned, then wildlife suffers. p  r Law of Syllogism

INVALID Examples: 1- If a rectangle has four congruent sides, then it is a square. p  q p: a rectangle has four congruent sides q: it is a square 2- A square has diagonals that are perpendicular. q  r 3- If a rectangle has four congruent sides, then its diagonals are perpendicular. 3- A rectangle has diagonals that are perpendicular. INVALID