Mastering Algebraic Reasoning Techniques for Success

Feb 25, 2025

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Learn advanced algebraic reasoning strategies to excel in solving complex problems. This course covers essential techniques and methods that will enhance your algebraic reasoning skills and boost your confidence in handling challenging algebraic problems.

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Mastering Algebraic Reasoning Techniques for Success

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Sec. 2-4 Reasoning in Algebra

Review properties of equality and use them to write algebraic proofs.Identify properties of equality and congruence. . Objectives. In Geometry you accept postulates

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2-4 Reasoning in Algebra

2-4 Reasoning in Algebra. Objectives: Use basic properties of algebra in reasoning Define congruence State the properties of congruence. Properties of Equality. Solve and Write a Justification for Each Step. 2 (x + 1) = 8 Given 2x + 2 = 8 Distributive Property

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2-5 Reasoning in Algebra and Geometry

2-5 Reasoning in Algebra and Geometry. *I can identify and use the properties of equality. (addition, subtraction, multiplication, division, reflexive, symmetric, transitive, and substitution.) *I can use the distributive property to justify combining like terms

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2.4 Properties of Algebra

Identity Property of Addition. The sum of any number and 0 is equal to thatnumber. Examples: 5 0 = 50 x = x2x 4 0 = 2x 40 3y 7 = 3y 7. Identity Property of Multiplication. The product of any number and 1 is equal to that number.Examples:1?5=5

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2.4 Deductive Reasoning

2.4 Deductive Reasoning. HW: Lesson 2.4/ 1 – 10, 13. Familiarize you with the deductive reasoning process Learn the relationship between inductive and deductive reasoning. Objectives. Problem Solving. Logic – The science of correct reasoning.

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2.4 Reasoning with Properties of Algebra

2.4 Reasoning with Properties of Algebra. Mrs. Spitz Geometry September 2004. Standards/Objectives:. Standard 3: Students will learn and apply geometric concepts. Objectives: Use properties from Algebra

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2.4 Reasoning with Properties from Algebra

2.4 Reasoning with Properties from Algebra. Algebraic Properties of Equality. Addition property: If a=b, then a+c = b+c. Subtraction property: If a=b, then a-c = b-c. Multiplication property: If a=b, then ac = bc. Division property: If a=b, and c≠0, then a/c = b/c. Writing reasons.

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2.4 Deductive Reasoning

2.4 Deductive Reasoning. Objective: To use the Law of Detachment and the Law of Syllogism. Deductive Reasoning. aka Logical Reasoning Definition : process of reasoning logically from given statements or facts to a conclusion. Law of Detachment.

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2.4 Deductive Reasoning

2.4 Deductive Reasoning. Deductive Reasoning – USES FACTS, RULES, DEFINITIONS AND PROPERTIES TO REACH A LOGICAL CONCLUSION. Deductive or Inductive?

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2.4 Reasoning in Algebra

2.4 Reasoning in Algebra. Chapter 2. Properties of Equality (pg 89 in text). Addition Property If a = b , then a + c = b + c Subtraction Property If a = b , then a – c = b – c Multiplication Property If a = b , then a · c = b · c

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Section 2-4: Reasoning in Algebra

Section 2-4: Reasoning in Algebra. Goal 2.01: Use logic and deductive reasoning to draw conclusions and solve problems. Turn in Homework. Lesson Quiz 2-3. Essential Question. How are properties of equality used in Algebraic and Geometric Proofs?. Addition Property of Equality.

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Lesson 2-4 Reasoning in Algebra

Lesson 2-4 Reasoning in Algebra. Check Skills You’ll Need. Name 1 in two other ways. Name the vertex of 2. If 1 2 , name the bisector of AOC. If m AOC = 90 and m 1 =45 , find m 2 If m AOC = 90 , name two perpendicular rays. A. 1. O. 2. B. C.

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2.4 Reasoning with Properties from Algebra

2.4 Reasoning with Properties from Algebra. Use properties of Algebra. Properties of Algebra. Addition Property If a = b, then a + c = b + c If x – 4 = 20, then x – 4 + 4 = 20 + 4. Properties of Algebra. Multiplication Property If a = b, then a * c = b * c where c ≠ 0

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Reasoning In Algebra

Reasoning In Algebra. Properties of Equality are accepted as true and are used to deductively prove conditional statements. Properties of Equality page 89. Addition Property Subtraction Property Multiplication Property Division Property Reflexive Property: a = a

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2-4 Reasoning in Algebra

2-4 Reasoning in Algebra. (7 cards). Addition/Subtraction Property. Add or subtract the same number from both sides of an equation 4 + x = 12 -4 -4 (Subtraction Property) X = 8. Multiplication/Division Property. Multiply or divide the same number on each side of an equation

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2-5 Reasoning in Algebra

Do Now: 1. Copy down HW. 2. Take out HW. 3. When two planes intersect, what does their intersection form? 4. How many points does it take to create a plane?. 2-5 Reasoning in Algebra. (7 cards). Addition/Subtraction Property. Add or subtract the same number from both sides of an equation

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2.4 Deductive Reasoning

2.4 Deductive Reasoning. Deductive Reasoning Sometimes called logical reasoning. The process of reasoning logically from given statements or facts to a conclusion. Drawing a conclusion based on several facts. Law of Detachment.

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2.4 DEDUCTIVE REASONING

2.4 DEDUCTIVE REASONING. Playing the game of logic well. Law of Detachment [(p>>q)^p]>>q. If p, then q is True And p is True Then q is True An example: If a vehicle is a car, then it has four wheels. A Cadillac is a car.

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2-4 Reasoning in Algebra

2-4 Reasoning in Algebra. Ex. 1 Justifying Steps. 1 . angle addition post. 2. substitution 3. simplify 4 . subtraction prop of = 5. division prop of =. Solve for x and justify 1. m<AOB + m<BOC = m<AOC 2. x + 2x + 10 = 139 3. 3x + 10 = 139 4. 3x = 129 5. x = 43. Ex. 1 Cont.

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Section 2.4: Reasoning with Properties from Algebra

Section 2.4: Reasoning with Properties from Algebra . Algebraic Properties of Equality. Properties are used to explain why certain steps are being taken, such as in solving an algebra equation. More Properties of Equality Used in Geometry.

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Section 2.4: Reasoning in Algebra

Section 2.4: Reasoning in Algebra. Objective: To connect reasoning in algebra and geometry. Reasoning in algebra. In Geometry, we accept postulates and properties as true. We use properties of equality to solve problems.

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2.4 Reasoning with Properties from Algebra (for geometry proof)

2.4 Reasoning with Properties from Algebra (for geometry proof). ?. p. 89. What are we doing, & Why are we doing this?. In algebra, you did things because you were told to…. In geometry, we can only do what we can PROVE… We will start by justifying algebra steps (because we already know how)

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