Reasoning with Properties from Algebra

Slides:

Advertisements

Similar presentations

2.5 Reasoning in Algebra and Geometry

Advertisements

Warm Up Solve each equation t – 7 = 8t (y – 5) – 20 = 0 x = 7 r = 12.2 or n = 17 y = 15.

Chapter 2 Properties from Algebra

2.5 Reasoning in Algebra and Geometry

2-5 Reasoning in Algebra and Geometry

2-6 Algebraic Proof p. 136 You used postulates about points, lines, and planes to write paragraph proofs. Use algebra to write two-column proofs. Use properties.

2-5 Reasoning in Algebra and Geometry

Reasoning with Properties of Algebra & Proving Statements About Segments CCSS: G-CO.12.

Introduction to Geometric Proof Logical Reasoning and Conditional Statements.

Algebraic proof Chapter 2 Section 6.

Honors Geometry Intro. to Deductive Reasoning. Reasoning based on observing patterns, as we did in the first section of Unit I, is called inductive reasoning.

Proving statements about angles

Over Lesson 2–5 5-Minute Check 1 In the figure shown, A, C, and lie in plane R, and B is on. Which option states the postulate that can be used to show.

2.4: Building a System of Geometric Knowledge

Postulates and Algebraic Proofs Advanced Geometry Deductive Reasoning Lesson 2.

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.

Section 2-4: Reasoning in Algebra TPI 32A: apply reflective, transitive, or symmetric prooperties of equality or congruence Objectives: Connect reasoning.

Lesson 2 – 6 Algebraic Proof

Lesson: 15 – 4 Preparing for Two-Column Proofs

Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a.

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.

BIG IDEA: Reasoning and Proof ESSENTIAL UNDERSTANDINGS: Logical reasoning from one step to another is essential in building a proof. Logical reasoning.

They are easier than Geometry ones!!. PROOFS The “GIVEN” is always written first –It is a “GIMME” The “PROVE” should be your last line Make a two column.

Bell Work If 2 Lines are skew, then they do not intersect 1) Converse 2) Inverse 3) Contrapositive 4) Biconditional.

2.6 Algebraic Proof. Objectives Use algebra to write two-column proofs Use algebra to write two-column proofs Use properties of equality in geometry proofs.

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,

Holt Geometry 2-5 Algebraic Proof 2-5 Algebraic Proof Holt Geometry.

Intro to Proofs Unit IC Day 2. Do now Solve for x 5x – 18 = 3x + 2.

Using Properties from Algebra to Prove Statements Section 2.5.

Postulate: A statement that is accepted without proof Theorem: An important statement that can be proven.

Geometry: Section 2.4 Algebraic Reasoning. What you will learn: 1. Use Algebraic Properties of Equality to justify the steps in solving an equation. 2.

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)

Section 2.7 Notes: Proving Segment Relationships Common Core State Standards G.CO.9 Prove theorems about lines and angles. Student Learning Targets 1.

2-5 Reasoning in Algebra and Geometry 2.5 Reasoning in Alg and Geo.

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

Chapter 2 Reasoning and Proof

Reasoning in Algebra and Geometry

2.5 and 2.6 Properties of Equality and Congruence

2.5 Algebraic Proof Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction.

Objectives Students will…

2.3 Proving Theorems Midpoint & Angle Bisector Theorem

2.5 Proving Statements about Segments and Angles

2-5 Reason Using Properties from Algebra

1. SWBAT use algebra to write two column proofs

Topic 2: Reasoning and Proof

2.5 Reasoning in Algebra and Geometry

Prove Statements about Segments and Angles

Section 2-4: Reasoning in Algebra

2-5 Algebraic Proof.

Chapter 2.5 Reasoning in Algebra and Geometry

LESSON 2–6 Algebraic Proof.

2-5 Algebraic Proof Are You? Ready Lesson Presentation Lesson Quiz

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.

Day 5 – Introduction to Proofs

Reasoning in Algebra & Geometry

2-6 Prove Statements About Segments and Angles

2-6 Algebraic Proof Use algebra to write two-column proofs.

2.4 Building a System of Geometry Knowledge

Prove Statements about Segments and Angles

2-5 Algebraic Proof Geometry.

Proving Statements about Segments

Presentation transcript:

Reasoning with Properties from Algebra BIG IDEA: Reasoning and Proof ESSENTIAL UNDERSTANDINGS: Logical reasoning from one step to another is essential in building a proof. Reasons in a proof include given information, definitions, properties, postulates, and previously proven theorems. MATHEMATICAL PRACTICE: Construct viable arguments and critique the reasoning of others

GETTING READY Follow the steps of the brainteaser using your age. Then try it using a family member’s age. What do you notice? Explain how the brainteaser works. Write down your age. Multiply it by 10. Add 8 to the product. Double that answer and then subtract 16. Finally, divide the result by 2.

Algebraic Properties of Equality Let be real numbers. Addition Property: Subtraction Property: Multiplication Property: Division Property: Reflexive Property: Symmetric Property: Transitive Property: Substitution Property: Distributive Property:

EX 1: What is the value of x? Justify each step.

EX 1: What is the value of x? Justify each step. b)

Math Background The properties of equality reviewed in the beginning of this lesson add to the students’ “toolbox” for writing proofs using deductive reasoning. It is important to make a connection between the algebraic proofs that you unknowingly completed throughout all of Algebra and the proofs that you will complete in Geometry. You should understand that the process of solving an equation is an algebraic proof, although the justifications for each step are not generally written down. Therefore, proofs are not unique to Geometry.

Properties of Congruence Reflexive Property: Symmetric Property: Transitive Property: Properties of equality are true for any numbers, while congruence properties are true for geometric figures

Example 2 a) Statements Reasons 1. Given 2. 3. 4. 4. Segment Addition Postulate 5. 6.

Example 2 b) A baseball diamond is shown below. The pitcher’s mound is at . Use the information to find the .

Proofs Proof: a convincing __________________ that uses ____________________ reasoning. A proof __________________ shows why a conjecture is __________ Two-column proof: lists each __________________ on the __________and the justification or ____________ for each statement is on the __________. Each statement must follow ______________________ from the __________ before it.

Writing a Two-Column Proof Given: Prove: Statements Reasons 1. 1. Given 2. 3. 3. Addition Property of Equality 4. 5.

Writing a Two-Column Proof Given: Prove: Statements Reasons 1. Given 2. 3.

2.4 p. 99 10 – 14 all, 16 – 28 evens, 29 – 32 all, 36 – 45x3 20 questions