Properties of Equality

Slides:

Advertisements

Similar presentations

September 8, 2011 "The way to be nothing is to do nothing." -- Nathaniel Howe Test prep, p. 18 #

Advertisements

1 2-4 Reasoning in Algebra Objectives: Use basic properties of algebra in reasoning Define congruence State the properties of congruence.

3-4 Algebra Properties Used in Geometry The properties of operations of real numbers that you used in arithmetic and algebra can be applied in geometry.

Chapter 2 Properties from Algebra

2.5 Reasoning in Algebra and Geometry

Properties of Real Numbers

PROPERTIES REVIEW!. MULTIPLICATION PROPERTY OF EQUALITY.

Properties of Equality, Identity, and Operations.

Properties of Equality

Algebraic proof Chapter 2 Section 6.

Reasoning with Properties from Algebra. Properties of Equality Addition (Subtraction) Property of Equality If a = b, then: a + c = b + c a – c = b – c.

2.5 – Reasoning Using Properties of Algebra

Section 2-4 Reasoning with Properties from Algebra.

Properties and Mental Computation p. 80. Math talk What are some math properties that we use? Why do you think we have them? Do you ever use them?

Section 2.4: Reasoning in Algebra

Chapter 2 Section 5. Objective  Students will make a connection between reasoning in Algebra and reasoning in Geometry.

Chapter 2 Section 4 Reasoning in Algebra. Properties of Equality Addition Property of Equality If, then. Example: ADD 5 to both sides! Subtraction Property.

Properties of Real Numbers

Reasoning With Properties of Algebra

Lesson 2 – 6 Algebraic Proof

Geometry 2.5 Big Idea: Reason Using Properties from Algebra.

Chapter 2.5 Notes: Reason Using Properties from Algebra Goal: You will use algebraic properties in logical arguments.

Unit 2 Reasoning with Equations and Inequalities.

2.3 Diagrams and 2.4 Algebraic Reasoning. You will hand this in P. 88, 23.

1.6. DEFINITIONS  An equation is a statement that two expressions are equal.  Usually contains 1 or more variables  A variable is a symbol that represents.

Warm Up. Warm Up Answers Theorem and Proof A theorem is a statement or conjecture that has been shown to be true. A theorem is a statement or conjecture.

GEOMETRY CHAPTER 2 Deductive Reasoning pages

SECTION 2-6 Algebraic Proofs JIM SMITH JCHS. Properties we’ll be needing REFLEXIVE -- a=a SYMMETRIC -- if x=2 then 2=x TRANSITIVE -- if a=b and b=c then.

Unit 2 Solve Equations and Systems of Equations

Linear Equations and Inequalities in One Variable What is an equation? =

Proofs!!! Ok just little ones :) Properties of Equality Addition Property –If a = b, then a + c = b + c Subtraction Property –If a = b, then a - c =

Objective: To prove and apply theorems about angles Proving Angles Congruent (2-6)

Reasoning with Properties from Algebra Algebraic Properties of Equality let a, b, and c be real numbers. Addition Property: If a=b, then a+c=b+c. Subtraction.

Chapter 2: Reasoning & Proof 2.4 Reasoning in Algebra.

Reasoning with Properties from Algebra. Properties of Equality For all properties, a, b, & c are real #s. Addition property of equality- if a=b, then.

Given an equation, you can … * Add the same value (or equivalent values) to both sides, If a = b, then a + 7 = b + 7 * Subtract the same value (or equivalent.

2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will help you solve problems and justify each step. In Geometry,

Reasoning in Algebra Chapter 2: Reasoning and Proof1 Objectives 1 To connect reasoning in algebra and geometry.

2.5 Reasoning and Algebra. Addition Property If A = B then A + C = B + C.

Ch 2-5 Reasoning in Geometry and Algebra

2.5 Algebra Reasoning. Addition Property: if a=b, then a+c = b+c Addition Property: if a=b, then a+c = b+c Subtraction Property: if a=b, then a-c = b-c.

Section 2.2 Day 1. A) Algebraic Properties of Equality Let a, b, and c be real numbers: 1) Addition Property – If a = b, then a + c = b + c Use them 2)

Lesson 1-3 Solving Equations. Properties of Equality Reflexive Propertya = a Symmetric PropertyIf a = b, then b = a. Transitive PropertyIf a = b and b.

Algebraic Proofs. 1. Transitive property of equality 2. Symmetric property of equality 3. Reflexive property of equality 4. Substitution 5. Addition property.

2-6: Algebraic Proof. Properties Reflexive property – every # equals itself; a=a, 1=1, etc. Symmetric property – You can switch the sides of the equation.

Reasoning in Algebra and Geometry

Objective The student will be able to:

Write a two-column proof

2.4 Objective: The student will be able to:

2.5 and 2.6 Properties of Equality and Congruence

2.5 Reasoning with properties from Algebra

2.5 – Reasoning Using Properties of Algebra

2.4 Algebraic Reasoning.

2-5 Reason Using Properties from Algebra

Reasoning With Properties of Algebra

2.5 Reasoning in Algebra and Geometry

2. Definition of congruent segments AB = CD 2.

Prove Statements about Segments and Angles

Reasoning With Properties of Algebra

PROPERTIES OF ALGEBRA.

Standard: MCC9-12.A.REI.1 – Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step,

Algebraic proofs A proof is an argument that uses logic to show that a conclusion is true. Every time you solved an equation in Algebra you were performing.

2.5 Reasoning Using Properties from Algebra

Properties of Equality Algebra

Properties of Numbers Lesson 1-3.

Reasoning with Properties from Algebra

Objective The student will be able to:

2-6: Algebraic Proof.

2-5 Algebraic Proof Geometry.

Presentation transcript:

Properties of Equality Notes 2.5 Properties of Equality

Addition and Subtraction Properties of Equality If a = b, then a + c = b + c If a = b, then a - c = b - c

Multiplication and Division Properties of Equality If a = b, then ac = bc If a = b, then a/c = b/c

Reflexive Property of Equality a = a Anything equals itself

Symmetric Property of Equality If a = b, then b = a Mirror Image

Transitive Property of Equality If a = b and b = c, then a = c

Substitution Property of Equality If a = b, then b may be substituted for a in any expression.

Distributive Property of Equality a(b + c) = ab + ac a(b – c) = ab - ac

Given: 2x+5 = 17 Prove x = 6 Statement Reason 1) 2x + 5 = 17 1) Given 2) Subtract = 3) X = 6 3) Division =

Given: 4x+5 = 6x - 9 Prove x = 7 Statement Reason 1) 4x + 5 = 6x - 9 2) Subtract = 3) 14 = 2x 3) Add = 4) Division = 4) X = 7