2-5 Algebraic proofs. SAT Problem of the day The volume and surface area of a cube are equal. What is the length of an edge of this cube? A) 1 B) 2 C)4.

Slides:

Advertisements

Similar presentations

2.5 Reasoning in Algebra and Geometry

Advertisements

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

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

Warm Up Solve each equation. 1. 3x + 5 = r – 3.5 = 8.7

Chapter 2 Properties from Algebra

2.5 Reasoning in Algebra and Geometry

2-5 Reasoning in Algebra and Geometry

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Algebraic proof Chapter 2 Section 6.

Algebraic Proofs. Warm Up Solve each equation. 1. 3x + 5 = r – 3.5 = t – 7 = 8t (y – 5) – 20 = 0 x = 4 r = 12.2 n = –38 y = 15.

 Solve and algebraic equation and provide a justification for each step.  Identify which property of equality or congruence is being used.

Obj. 7 Algebraic Proof proof – an argument which uses logic, definitions, properties, and previously proven statements algebraic proof – A proof which.

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Section 2.4: Reasoning in Algebra

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

2-3 Algebraic Proof Section 2.3 Holt McDougal Geometry Holt Geometry.

Objectives Review properties of equality and use them to write algebraic proofs.

Holt Geometry 2-5 Algebraic Proof 2-5 Algebraic Proof Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Lesson 2 – 6 Algebraic Proof

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.

2-5 Reasoning with Properties from Algebraic Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

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.

2.4 Reasoning with Properties from Algebra (for geometry proof) p. 89 ?

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.

Prove Your Proof! UNIT 2. Do Now Solve the following one variable equations: ◦4m – 8 = -12 ◦X – 3.5 = 8.7 ◦4x – 7 = 8x + 3 ◦(x+8)/5 = -6 ◦2(x – 5) – 20.

For numbers 1 & 2 Solve for x and give a reason listed below for each step 1)4m - 8 = -12 2)6r – 3 = -2 ( r + 1 )

2.4 Reasoning with Properties from Algebra ?. What are we doing, & Why are we doing this?  In algebra, you did things because you were told to….  In.

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

Holt Geometry 2-5 Algebraic Proof Warm Up Solve each equation. 1. 3x + 5 = t – 7 = 8t (y – 5) – 20 = 0 x = 4 n = –38 y = 15 t = – 5252.

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.

Holt McDougal Geometry 2-5 Algebraic Proof Review properties of equality and use them to write algebraic proofs. Identify properties of equality and congruence.

Chapter 2 Reasoning and Proof

Lesson 2-5: Algebraic Proofs

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…

Chapter 2.6 (Part 1): Prove Statements about Segments and Angles

9. Deductive D Inductive H Invalid Valid (2.5, 3.5)

2.4 Algebraic Reasoning.

Chapter Notes: Properties and Algebraic Proofs

Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

2.5 Reasoning in Algebra and Geometry

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Lesson 2-5: Algebraic Proofs

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Chapter 2: Geometric Reasoning

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

2-5 Algebraic Proof.

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Chapter 2.5 Reasoning in Algebra and Geometry

Warm Up Determine whether each statement is true or false. If false, give a counterexample. 1. It two angles are complementary, then they are not congruent.

2.4 Vocabulary equation “solve” an equation mathematical reasoning

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

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

2.4 Vocabulary equation “solve” an equation formula

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Warm Up Solve each equation. 1. 3x + 5 = r – 3.5 = 8.7

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Day 5 – Introduction to Proofs

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Warm Up Solve each equation. 1. 3x + 5 = r – 3.5 = 8.7

UNIT 2 Algebraic Proofs A proof is an argument that uses logic, definitions, properties, and previously.

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Objective SWBAT use the properties of equality to write algebraic proofs. HW Page 107 {3-15 odd, 23, 25, 31}

Warm Up Solve each equation. 1. 3x + 5 = r – 3.5 = 8.7

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Presentation transcript:

2-5 Algebraic proofs

SAT Problem of the day The volume and surface area of a cube are equal. What is the length of an edge of this cube? A) 1 B) 2 C)4 D)6 E)9

SAT problem of the day Answer :D

Objectives * Review properties of equality and use them to write algebraic proofs. *Identify properties of equality and congruence.

What are Proofs? A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true. An important part of writing a proof is giving justifications to show that every step is valid.

Properties

The Distributive Property states that: a(b + c) = ab + ac.

Example#1 Solve the equation 4m – 8 = –12. Write a justification for each step. 4m – 8 = –12 Given equation Addition Property of Equality 4m = –4 Simplify. m =–1 Simplify. Division Property of Equality

Example#2 Solve the equation. Write a justification for each step. Given equationMultiplication Property of Equality. t = –14Simplify.

Example#3

Example#4

Student Guided Practice Do problems 2-7 on your book page 107

Applications

What is the temperature in degrees Celsius C when it is 86°F? Solve the equation C = 5/9(F – 32) for C and justify each step.

Algebraic proofs in geometry Like algebra, geometry also uses numbers, variables, and operations. For example, segment lengths and angle measures are numbers. So you can use these same properties of equality to write algebraic proofs in geometry.

Properties A ____________ B AB represents the length AB, so you can think of AB as a variable representing a number.

Geometric properties You learned in Chapter 1 that segments with equal lengths are congruent and that angles with equal measures are congruent. So the Reflexive, Symmetric, and Transitive Properties of Equality have corresponding properties of congruence.

Example#5 Write a justification for each step. NO = NM + MO

Example#6 Write a justification for each step. mABC = mABD + mDBC

Student Guided Practice Do Problems 10 and 11 from page 107 on your book

Homework!! Do problems from page 108

Closure Today we learned about algebraic proofs and how to justify each step. Next class we are going to learned about geometric proofs