Section 2.2 Definitions and Biconditional Statement

Slides:

Advertisements

Similar presentations

Geometry 2.2 Big Idea: Analyze Conditional Statements

Advertisements

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

CAHSEE W. UP GEOMTRY GAME PLAN Date9/24/13 Tuesday Section / TopicNotes #19: 2.2 Definitions & Biconditional Statements Lesson GoalSTUDENTS WILL BE ABLE.

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.

Notes on Logic Continued

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.

Unit 3 Lesson 2.2: Biconditionals

CHAPTER 1: Points, Lines, Planes, and Angles

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,

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

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

2.2 Definition and Biconditional Statements Use definitions and biconditional statements.

Conditional Statements Lesson 2-1. Conditional Statements have two parts: Hypothesis ( denoted by p) and Conclusion ( denoted by q)

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.

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

Section 2.2 Conditional Statements 1 Goals Recognize and analyze a conditional statement Write postulates about points, lines, and planes using conditional.

Chapter 2.2 Notes: Analyze Conditional Statements Goal: You will write definitions as conditional statements.

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

Unit 01 – Lesson 07 – Conditional Statements

Warm up 1.Re-write the following statements as an if-then statement. 2.State the converse of the statement. a.The midpoint of a segment is a point that.

Chapter 2 Section 2 Biconditionals and Definitions.

Recall Section 2-3: Biconditionals & Definitions Objectives:

2.2 Definitions and Biconditional Statements

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.

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.

2.4 Biconditional Statements and Definitions Textbook pg 96.

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?

Perpendicular Lines SECTION 2.5.

Postulates and Theorems Relating Points, Lines, and Planes

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.

2-3 Biconditionals and Definitions Objective: To write biconditionals and recognize good definitions.

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

Lesson 2-1 Conditional Statements 1 Lesson 2-3 Conditional Statements.

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

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

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

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

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.

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)

Conditional & Biconditional Statements Chapter 2 Section 2 1.

Conditional & Biconditional Statements Chapter 2 Section 4.

Objective Write and analyze biconditional statements.

2.2 Definitions and Biconditional Statements

Conditional Statements

Conditional Statements

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

Section 2-2 (cont.) Definitions

Definitions and Biconditional Statements

EXAMPLE 4 Write a biconditional

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

Section 2.2 Definitions and Biconditionals

Conditional Statements

2.2 Definitions and Biconditional Statements

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

Last Night’s Homework: 2.2 Handout Tonight’s Homework: 2.3 Handout

Chapter 2.2 Notes: Analyze Conditional Statements

G7 Conditional Statements

2.1 Continued: Definitions and Biconditionals

Different Forms of Conditional Statements

Presentation transcript:

Section 2.2 Definitions and Biconditional Statement

Definition of Perpendicular Lines Two lines that intersect to form a right angle.

Definition of a Line Perpendicular to a Plane A line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it.

Definitions are Forward and Backward All definitions can be interpreted “forward” and “backward.” If two lines are perpendicular, then they intersect to form a right angle OR If two lines intersect to form a right angle, then they are perpendicular.

Biconditional Statements Not all conditional statements are written in the If-Then form. Biconditional statements are conditional statements too. A biconditional statement contains the phrase, “if and only if” OR “iff” Ex. 1 The light is on if and only if the light switch is up.

Biconditional Statement (continued-) Writing a biconditional statement is equivalent to writing a conditional statement and its converse. If-then Cond. State. (forward) If the light is on, then the light switch is up. Converse (backward) If the light switch is up, then the light is on.

Facts on Biconditional Statements Biconditional statements can be either TRUE or FALSE. To be TRUE, BOTH the conditional statement and its converse must be true. Therefore, ALL true biconditional statements are True both forward and backward. All definitions can be written as true biconditional statements.

Why are Biconditional Statements Important? If you can write a true biconditional statement, then you can use the conditional statement- “If-Then” or the converse to justify an argument.