2.1 If-Then Statements; Converses

Slides:

Advertisements

Similar presentations

Beat the Computer! Geometry Vocabulary and Formulas for Unit 1

Advertisements

Proving Statements in Geometry

What is the length of AB What is length of CD

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.

Chapter 2 Reasoning and Proof Chapter 2: Reasoning and Proof.

Bell Work 1) Write the statement in “If/Then” Form. Then write the inverse, converse, and contrapositive: a) A linear pair of angles is supplementary.

a location in space that has no size.

Biconditional Statements and Definitions 2-4

Unit 3 Lesson 2.2: Biconditionals

Unit 2: Deductive Reasoning

Chapter 2 Review Reasoning and Proof.

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

10/21/2015Geometry1 Section 2.1 Conditional Statements.

Do Now Each of the letters stands for a different digit. The first digit in a number is never zero. Replace the letters so that each sum is correct.

Reasoning and Conditional Statements Advanced Geometry Deductive Reasoning Lesson 1.

Logic and Proofs. 2-2 Conditional Statements Conditional statements are just that – statements that contain a condition. If p then q p is the Hypothesis.

Deductive Reasoning “The proof is in the pudding.” “Indubitably.” Je solve le crime. Pompt de pompt pompt." Le pompt de pompt le solve de crime!" 2-1 Written.

2.2 Write Definitions as Conditional Statements

Section 2-1 Using Deductive Reasoning. If/then statements Called conditional statements or simply conditionals. Have a hypothesis (p) and a conclusion.

Boyd/Usilton. Conditional If-then statement that contains a hypothesis (p) and a conclusion (q). Hypothesis(p): The part of the conditional following.

Test 1 Review Geometry Thursday 9/9/10. Quiz 1 1. Write the following statement as a conditional. Write the hypothesis and the conclusion. Glass objects.

2.2 Definitions and Biconditional Statements

1 If-then Statements “If-then statements” are also called “Conditional Statements” or just “Conditionals” “If-then statements” are also called “Conditional.

CHAPTER 2: DEDUCTIVE REASONING Section 2-1: If-Then Statements; Converses.

Unit 2 Reasoning and Proof “One meets his destiny often in the road he takes to avoid it.” ~ French Proverb.

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

2.1 Conditional Statements Ms. Kelly Fall Standards/Objectives: Students will learn and apply geometric concepts. Objectives: Recognize the hypothesis.

GEOMETRIC PROOFS A Keystone Geometry Mini-Unit. Geometric Proofs – An Intro Why do we have to learn “Proofs”? A proof is an argument, a justification,

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.

Chapter 1 - Warm-ups 09/03 page 7 #1-10 all (WE) 09/08 page 14 #1-20 all (CE) 09/12 page 20 #2-26 even (CE) 09/16 Self-Test 2 page 29 #1-12 all.

 When a conditional and its converse are both true, we combine them to make a biconditional.  Example:  Biconditional – An angle is right if and only.

Geometry Review 1 st Quarter Definitions Theorems Parts of Proofs Parts of Proofs.

GEOMETRY CHAPTER 2 Deductive Reasoning pages

Lesson 2 – 5 Postulates and Paragraph Proofs

2.3 Biconditionals and Definitions 10/8/12 A biconditional is a single true statement that combines a true conditional and its true converse. You can join.

Holt Geometry 2-6 Geometric Proof Warm Up Determine whether each statement is true or false. If false, give a counterexample. 1. It two angles are complementary,

Chapter 2 Section 2.1 – Conditional Statements Objectives: To recognize conditional statements To write converses of conditional statements.

2-3 Biconditionals and Defintions. Biconditional- a statement that is the combination of a conditional statement and its converse. If the truth value.

DefinitionsTrue / False Postulates and Theorems Lines and Angles Proof.

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

Basics of Geometry Chapter Points, Lines, and Planes Three undefined terms in Geometry: Point: No size, no shape, only LOCATION.  Named by a single.

Deductive Reasoning “The proof is in the pudding.” “Indubitably.” Je solve le crime. Pompt de pompt pompt." Le pompt de pompt le solve de crime!" 2-1 Classroom.

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.

2.2 Definitions and Biconditional Statements GOAL 1 Recognize and use definitionsGOAL 2 Recognize and use biconditional statements. What you should learn.

2-1 I F -T HEN S TATEMENTS AND C ONVERSES  Chapter 2 Test: Monday Oct. 1 st  Quiz: Wed. Sept. 26  Start today’s notes in current notes section.

Chapter 2: Deductive Reasoning. -The process of reasoning from one or more general statements to reach a logically certain conclusion.

Biconditional Statements p q. Biconditional Statements p q {P iff q} P, if and only if q Is equivalent to both: If p, then q If q, then p P, if and only.

It’s already Tuesday! 1. You need your journal. Unit 1 test is on Friday What did the one wall say to the other wall? I’ll meet you at the corner.

2-1 CONDITIONAL STATEMENTS

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

WARM UP 01/09/17 Go over the words and write the Definition of each:

2.2 Definitions and Biconditional Statements

Unit 2: Deductive Reasoning

definition of a midpoint

Conditional Statements

Conditional Statements

ANSWERS TO EVENS If angle 1 is obtuse, then angle 1 = 120

2.1 Conditional Statements

2.2 Analyze Conditional Statements

Conditional Statements

2.2 Definitions and Biconditional Statements

1.3 Segments, Rays, and Distance

CHAPTER 2: DEDUCTIVE REASONING

Reasoning and Proofs Deductive Reasoning Conditional Statement

G7 Conditional Statements

2.4 Conditional Statements

Chapter 2 Reasoning and Proof.

Presentation transcript:

2.1 If-Then Statements; Converses Geometry 2.1 If-Then Statements; Converses

This is the first introduction to logical reasoning……… The foundation of doing well in Geometry is knowing what the words mean.

In Geometry, a student might read, “If B is between A and C, then AB + BC = AC (You know this as the Segment Addition Postulate)

If-Then To represent if-then statements symbolically, we use the basic form below: If p, then q. p: hypothesis q: conclusion

True or false? If you live in San Francisco, then you live in California. True

Converse The converse of a conditional is formed by switching the hypothesis and the conclusion: Statement: If p, then q. Converse: If q, then p. hypothesis conclusion

A counterexample is an example where the hypothesis is true, but the conclusion is false. It takes only ONE counterexample to disprove a statement.

State whether each conditional is true or false State whether each conditional is true or false. If false, find a counterexample. Statement: If you live in San Francisco, then you live in California. True Converse: If you live in California, then you live in San Francisco. False Statement: If points are coplanar, then they are collinear. Converse: If points are collinear, then they are coplanar. If AB BC, then B is the midpoint of AC. Converse: If B is the midpoint of AC, then AB BC. These make the hypothesis true and conclusion false. Counterexample: You live in Danville, Alamo, Livermore, etc. . It makes the hypothesis true and conclusion is false. . . Counterexample: B. It makes the hypothesis true and conclusion false. A . .C Counterexample:

Find a counterexample If a line lies in a vertical plane, then the line is vertical. If x2 = 49, then x = 7. Counterexample: x = -7 It makes the hypothesis true and conclusion false. Counterexample: It makes the hypothesis true and conclusion false.

Other Forms of Conditional Statements General form Example If p, then q. If 6x = 18, then x = 3. p implies q. 6x = 18 implies x = 3. p only if q. 6x = 18 only if x = 3. q if p. x = 3 if 6x = 18. These all say the same thing.

The Biconditional If a conditional and its converse are BOTH TRUE, then they can be combined into a single statement using the words “if and only if.” This is a biconditional. p if and only if q. p q. Example: Tomorrow is Saturday if and only if today is Friday.

The Biconditional as a Definition A ray is an angle bisector if and only if it divides the angle into two congruent angles.

Homework P. 35 #1-29 Odd Read 2.2 P. 40 CE 1-11