Section 2-2 (cont.) Definitions

Slides:

Advertisements

Similar presentations

Notes on Logic Continued

Advertisements

Use the following conditional for Exercises 1–3. If a circle’s radius is 2 m, then its diameter is 4 m. 1.Identify the hypothesis and conclusion. Hypothesis:

Check your skills 2. Homework Check Notes 4. Practice 5. Homework/work on Projects.

Conditional Statements

GEOMETRY Chapter 2 Notes.

2-3 Biconditionals and Definitions

2.3 Biconditionals and Definitions

Identify the hypothesis and the conclusion of each conditional statement. 1.If x > 10, then x > 5. 2.If you live in Milwaukee, then you live in Wisconsin.

Biconditionals & Definitions. Biconditional Statement Contains the phrase “if & only if” Abbr. iff It is a conditional statement & its converse all in.

Identify the hypothesis and the conclusion of each conditional statement. 1.If x > 10, then x > 5. 2.If you live in Milwaukee, then you live in Wisconsin.

1 Biconditional Statements Define and write biconditionals State the characteristics of good definitions.

2.2 Definition and Biconditional Statements Use definitions and biconditional statements.

Section 2-4: Biconditionals and Good Definitions Rigor – Write Biconditional statements and differentiate between a good or bad definition. Relevance –

1 2.2 Definitions & Biconditional Statements Objective: To write biconditionals and recognize good definitions.

Chapter 2 Review. Conditional statements have a IF and a THEN. 2 Hypothesis Conclusion.

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

2.2 Definitions and Biconditional Statements. Definition Two lines are called perpendicular lines if they intersect to form a right angle. A line perpendicular.

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

Section 2-2: Biconditional and Definitions TPI 32C: Use inductive and deductive reasoning to make conjectures Objectives: Write the inverse and contrapositive.

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

Section 2-1 Conditional Statements. Conditional statements Have two parts: 1. Hypothesis (p) 2. Conclusion (q)

Day 3. Warm Up Find the distance and midpoint between the two points below.

Chapter 2 Section 2 Biconditionals and Definitions.

Recall Section 2-3: Biconditionals & Definitions Objectives:

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.

Chapter 2: Reasoning & Proof 2.2 Biconditionals & Definitions.

 If an integer ends with 0, then the integer is divisible by 2.  What is the truth value of the above conditional?  What is the converse?  What is.

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.

 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.

B ICONDITIONALS AND DEFINITIONS BIG IDEA: REASONING AND PROOF ESSENTIAL UNDERSTANDINGS: A definition is good if it can be written as a biconditional. Every.

[2-3] Biconditionals & Definitions

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.

Conditional Statments. Warm Up What is the fourth point of plane XUR Name the intersection of planes QUV and QTX Are point U and S collinear?

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

Section 2.1 Geometric Statements. Definitions: Conditionals, Hypothesis, & Conclusions: A conditional statement is a logical statement that has two parts:

Reasoning and Proof DAY 3: 2.3 Biconditional Statements.

Lesson 2-3 BICONDITIONAL STATEMENTS AND DEFINITIONS.

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

CONDITIONAL STATEMENTS Section 2-1. Objectives  To recognize conditional statements.  To write converses of conditional statements.

Inductive and Deductive Reasoning. Notecard 30 Definition: Conjecture: an unproven statement that is based on observations or given information.

EXAMPLE 4 Write a biconditional Write the definition of perpendicular lines as a biconditional. SOLUTION Definition: If two lines intersect to form a right.

2.3 Biconditionals and Definitions

Section 2.2 Homework Quiz Question Put the following Conditional Statement into If Then Form: All birds have feathers.

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.

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

Bell Work Find the hypothesis and conclusion 1) If the class behaves, then Mr. Liu will give all the students 5 point extra credit Find the converse 2)

Biconditionals and Definitions. Warm-up Write the converse, inverse and contrapositive of the following conditional. If Boulder gets 15 inches of rain,

2-2 B ICONDITIONALS & D EFINITIONS M11.B.2 O BJECTIVES : 1) T O WRITE BICONDITIONALS 2) T O RECOGNIZE GOOD DEFINITIONS.

Conditional & Biconditional Statements Chapter 2 Section 4.

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

Bi-conditionals and Definitions Chapter 2: Reasoning and Proof1 Objectives 1 To write bi-conditionals 2 To recognize good definitions.

BELL-WORK Get a laptop! Go to clever.com/in/scs!

Analyze Conditional Statements

Biconditionals & Deductive Reasoning

Conditional Statements

Definitions and Biconditional Statements

Biconditionals and definitions

EXAMPLE 4 Write a biconditional

2-3: Biconditionals and Definitions

Biconditionals and Definitions

Good definitions are important in geometry (and almost every area) 

Section 2-4: Biconditionals and Good Definitions

Section 2-4: Biconditionals and Good Definitions

Drill Draw a segment so that A and C are the endpoints and B is somewhere between them. If AB is 10 feet and BC is 18 feet, how long is AC? If AB is 2x.

Biconditionals and Definitions

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

Conditional Statements

Section 2.2 Definitions and Biconditional Statement

Biconditionals and Definitions

Presentation transcript:

Section 2-2 (cont.) Definitions

Definition Activity Work with your surrounding classmates and write the definition for a “Polyglob.”

Good Definitions A good definition uses clearly understood terms. The terms should be commonly understood or already defined. A good definition is precise. Good definitions avoid words such as large, sort of, and almost. A good definition is reversible. That means that you can write a good definition as a true biconditional.

Example (Me) Show that this definition of perpendicular lines is reversible. Then write it as a true biconditional. Definition: Perpendicular lines are two line that intersect to form right angles. Conditional: If two lines are perpendicular, then they intersect to form right angles. Converse: If two lines intersect to form right angles, then they are perpendicular. Biconditional: Two lines are perpendicular if and only if they intersect to form right angles.

Example (We) Definition: An airplane is a vehicle that flies. Conditional: Converse: If it is an airplane, it is a vehicle that flies. True If it is a vehicle that flies, then it is an airplane. False – counterexample: helicopter

Example (You) Definition: A right angle is an angle whose measure is 90. Conditional: Converse: Biconditional:

Homework: Section 2-2 p.90 #’s 18-23, 33-37