2.1-2 Inductive Reasoning and Conditional Statements

Slides:

Advertisements

Similar presentations

Geometry 2.2 Big Idea: Analyze Conditional Statements

Advertisements

Conditional Statements

When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. Inductive reasoning is the process.

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.

Get Ready To Be Logical! 1. Books and notebooks out. 2. Supplies ready to go. 3. Answer the following: The sum of 2 positive integers is ___________ True.

2.2 Conditional Statements Goal: Students will be able:  To recognize conditional statements and their parts.  To write converses, inverses, and contrapositives.

2.2 Analyzing Conditional Statements. Conditional Statements: Conditional Statement (In “If-Then” form): “If it is a bird, then it has feathers.” Ex.

Conditional Statements

Geometry Unit 2 Power Points Montero to 2.3 Notes and Examples Patterns, Conditional Statements, and BiConditional Statements Essential Vocabulary.

Chapter Two Emma Risa Haley Kaitlin. 2.1 Inductive reasoning: find a pattern in specific cases and then write a conjecture Conjecture: unproven statement.

Logic and Reasoning. Identify the hypothesis and conclusion of each conditional. Example 1: Identifying the Parts of a Conditional Statement A.If today.

Lesson 2-2: Conditional Logic Summary Original “If …, then …” Conditional Statement Inverse Statement Converse Statement Contrapositive Statement Biconditional.

Inductive/Dedu ctive Reasoning Using reasoning in math and science.

2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning.

Conditional Statements

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.

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

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

Conditional Statements Chapter 2 Section 2. Conditional Statement A statement where a condition has to be met for a particular outcome to take place More.

Section 2-2: Conditional Statements. Conditional A statement that can be written in If-then form symbol: If p —>, then q.

Unit 01 – Lesson 07 – Conditional Statements

1.2 Inductive Reasoning. Inductive Reasoning If you were to see dark, towering clouds approaching what would you do? Why?

Unit 01 – Lesson 08 – Inductive Reasoning Essential Question  How can you use reasoning to solve problems? Scholars will  Make conjectures based on inductive.

Logic Inductive Reasoning Reasoning based on patterns you observe Example: What is the next number in the sequence 2, 4, 6, 8…?

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

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

Section 2.2 Inductive and Deductive Reasoning. Definition: Conjecture an unproven statement that is based on observations or given information.

Lesson 1.2 Inductive Reasoning Pages Observe Look for patterns Develop a hypothesis (or conjecture) Test your hypothesis.

2-2 Conditional Statements Objectives: To recognize conditional statements and their parts To write converses, inverses, and contrapositives of conditionals.

Inductive and Deductive Reasoning. Notecard 29 Definition: Conjecture: an unproven statement that is based on observations. You use inductive reasoning.

Conditional Statements Mrs. Spitz Modifyied by Mrs. Ortiz-Smith Geometry.

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.

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

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

Warm Up 1.) Adds one more side to the polygon. 2.)

Conditional Statements

Analyze Conditional Statements

Chapter 1 Lessons 1-4 to 1-8.

Conditional Statements

Warm Up For this conditional statement: If a polygon has 3 sides, then it is a triangle. Write the converse, the inverse, the contrapositive, and the.

Conditional Statements

Reasoning Proof and Chapter 2 If ….., then what?

Overview of related conditionals

Inductive and Deductive Reasoning

3 – 6 Inductive Reasoning.

2.2 Deductive Reasoning Objective:

2-2 Conditional Statements

Warmup Definition: Perpendicular Lines—

2.1 Conditional Statements

Conditional Statements

Patterns and Inductive Reasoning

Conditional Statements

2.3 Apply Deductive Reasoning

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

Reasoning and Proofs Deductive Reasoning Conditional Statement

G7 Conditional Statements

DRILL What would be the coordinates of the point (-2, 4) if it was reflected over the y-axis? If you dilate the point (-3, 9) using a scale factor of 1/3,

More Conditional Statements

Patterns and Inductive Reasoning

Patterns and Inductive Reasoning

Logic and Reasoning.

2-3 Conditional Statements

Angles, Angle Pairs, Conditionals, Inductive and Deductive Reasoning

Lesson 2.1 Use Inductive Reasoning

TODAY’S OBJECTIVE: Standard: MM1G2

2-1 Inductive Reasoning and Conjecture

Presentation transcript:

2.1-2 Inductive Reasoning and Conditional Statements Mrs. Vazquez Geometry

g-co.3.9-11 Essential Question: What terms should I be familiar with for the lesson? Objective: Students will be able to define and understand new vocabulary.

2.1 vocab conjecture: an unproven statement based on observations inductive reasoning: when you find a pattern in specific cases to write a conjecture to make a generalization counterexample: a specific case in which the conjecture is false

2.1 vocab examples conjecture: The sum of two numbers is always greater than the larger number. inductive reasoning: 1 + 3 = 4 ; 4 > 3 8 + 4 = 12 ; 12 > 8 10 + 50 = 60 ; 60 > 50 counterexample: -8 + (-2) = -10 ; -10 ≯ -2

2.2 VOcab conditional statement: a logical statement that has two parts & is written in if-then form hypothesis: the “if” of a conditional statement conclusion: the “then” of a conditional statement Example: If two ∡s form a linear pair, then they are supplementary. (hypothesis) , (conclusion)

2.2 VOcab negation: the opposite of the original statement Ex: Mrs. Vazquez is a strict teacher. negation: Mrs. Vazquez is not a strict teacher.

If you will study, then you will pass geometry. converse: the exchange of the hypothesis & the conclusion of a conditional statement If you will pass Geometry, then you will study. contrapositive: the negation of the converse If you will not pass Geometry, then you will not study. inverse: the negation of both the hypothesis & conclusion If you will not study, then you will not pass Geometry.

biconditional statement when a conditional statement & its converse are true a statement can be made that contains “if and only if” (iff). Ex: Conditional Statement. If two lines intersect to form a ∟, then they are ⊥. Converse. If two lines are ⊥, then they intersect to form a ∟. Biconditional Statement. Two lines are ⊥ iff they intersect to form a ∟.