2.3 Biconditionals and Definitions

Slides:

Advertisements

Similar presentations

Chapters 1 & 2 Theorem & Postulate Review Answers

Advertisements

Problems to study for the chapter 2 exam

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.

GEOMETRY Chapter 2 Notes.

Conditional Statements

(7.6) Geometry and spatial reasoning. The student compares and classifies shapes and solids using geometric vocabulary and properties. The student is expected.

2-3 Biconditionals and Definitions

Biconditional Statements and Definitions 2-4

Warm Up: For the given statement, determine the converse, inverse, and contrapositive. Assuming the given statement is true, determine if each new statement.

Honors Geometry Intro. to Geometric Proofs. Before we can consider geometric proofs, we need to review important definitions and postulates from Unit.

Which of the following values of x and y give the greatest value of z if z=x 2 -2y+106 ? a. x=-5, y=11b. x=2, y=0 c. x=3, y=-2d. x=5, y= warm-up.

GEOMETRY REVIEW Look how far we have come already!

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.

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.

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.

8-4 Angles in Polygons Problem of the Day How many different rectangles are in the figure shown? 100.

Proof Geometry.  All quadrilaterals have four sides.  They also have four angles.  The sum of the four angles totals 360°.  These properties are.

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

Chapter 1 Introduction to Geometry. Slide Getting Started Points – To name a point always use Lines – All lines are and extend in both directions.

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

Section 2-2: Biconditionals and Definitions Goal: Be able to write biconditionals and recognize definitions. Conditional Statement: ________________If.

Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your vegetables,

2.2.1 Analyze Conditional Statements and Proof Chapter 2: Reasoning and Proof.

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:

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.

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

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

Quadrilaterals I by Definition Polygon – a closed many straight- sided figure.

[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.

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

Lesson 2-3 BICONDITIONAL STATEMENTS AND DEFINITIONS.

Geometry Chapter 2 section 3 Pages # Biconditionals and Definitions. Standard addressed: Construct and judge the validity of a logical argument.

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.

Chapter 2 Introducing Geometry. Lesson 2.1 Definition – a statement that clarifies or explains the meaning of a word or a phrase. Point – an undefined.

2.3 Biconditionals and Definitions

Chapter 2, Section 1 Conditional Statements. Conditional Statement Also know as an “If-then” statement. If it’s Monday, then I will go to school. Hypothesis:

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

Conditional & Biconditional Statements Chapter 2 Section 4.

Geometry Chapter 2: Reasoning and Introduction to Proof We can do this dude!

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.

Objective Write and analyze biconditional statements.

Biconditionals Goal: To learn about and use biconditional statements

Subject Matter: Bi-conditionals and Definitions Objective Pacing

Biconditionals and definitions

2.3 Biconditionals, and Definitions

2.1: Patterns and Inductive Reasoning

2-3: Biconditionals and Definitions

2.2 Deductive Reasoning Objective:

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

Biconditional Statements and Definitions 2-4

Section 2-4: Biconditionals and Good Definitions

Section 2-4: Biconditionals and Good Definitions

Biconditional Statements and Definitions 2-4

Section 2-4: Biconditionals and Good Definitions

Biconditionals and Definitions

Quarterly Review!!.

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

Objective Write and analyze biconditional statements.

Biconditionals and Definitions

Presentation transcript:

2.3 Biconditionals and Definitions Geometry Chapter 2: Reasoning and Proof

Biconditional Single true statement that combines a true conditional and its true converse Conditional: If the sum of the measures of two angles is 180, then the two angles are supplementary. Converse: If two angles are supplementary, then the sum of the measures of the two angles is 180. Biconditional (Put it together): Two angles are supplementary if and only if the sum of the measures of the two angles is 180.

Represent! Conditional (p → q): If the sum of the measures of two angles is 180, then the two angles are supplementary. Converse (q → p): If two angles are supplementary, then the sum of the measures of the two angles is 180. Biconditional (p ↔ q): Two angles are supplementary if and only if the sum of the measures of the two angles is 180.

Let’s Work Together Conditional: If two angles have equal measures, then the angles are congruent. Converse: If two angles are congruent, then the angles have equal measures. Biconditional: Two angles have equal measures if and only if the angles are congruent.

Try It! Conditional: If two numbers are reciprocals, then their product is 1. Converse: If the product of two numbers is 1, then the numbers are reciprocals. Biconditional: Two numbers are reciprocals if and only if their product is 1.

Undo It A ray is an angle bisector if and only if it divides an angle into two congruent angles. p: A ray is an angle bisector q: A ray divides an angle into two congruent angles. p → q: If a ray is an angle bisector, then it divides an angle into two congruent angles. q → p: If a ray divides an angle into two congruent angles, then it is an angle bisector.

Your Turn! An integer is divisible by 100 if and only if its last two digits are zeros. p: An integer is divisible by 100 q: The last two digits of an integer are zeros. p → q: If an integer is divisible by 100, then its last two digits are zeros. q → p: If the last two digits of an integer are zeros, then it is divisible by 100.

DEFINITIONS A statement that can help you identify or classify an object. Good definition: Uses clearly understood terms Is precise (avoid words such as large, sort of, almost, etc.) Is reversible (true biconditional)

A straight angle is an angle that measures 180. Is it reversible? Write as a biconditional. An angle is a straight angle if and only if its measure is 180.

A quadrilateral is a polygon with four sides. Reversible? Biconditional: A figure is a quadrilateral if and only if it is a polygon with four sides.

Is it Good? Which of the following is a good definition? A fish is an animal that swims. Rectangles have four corners. Giraffes are animals with very long necks A penny is a coin worth one cent.

Practice Problems 22 problem Worksheet Conditionals Converse Inverse Contrapositive Biconditionals Definitions