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.

Slides:

Advertisements

Similar presentations

Advertisements

Bell Ringer 11-8 (in your notes) You may use your notes on 2-7 only. 1.What is the title of Lesson 2-7? 2.What is the difference between a postulate and.

2.6 Prove Statements About Segments and Angles

Algebraic Properties Copy the following on a clean sheet of paper PropertyDescription Reflexive PropertyFor every number a, a = a Symmetric PropertyFor.

2.5 Proving Statements about Segments

Lesson 2-6 Algebraic Proofs. Ohio Content Standards:

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.

Lesson 2-6 Algebraic Proof. 5-Minute Check on Lesson 2-5 Transparency 2-6 In the figure shown, A, C, and DH lie in plane R, and B is on AC. State the.

Turn in all binders, Math Whiz Punch Cards and HW paragraphs on How and Why do we create things? What are the consequences? Bell Ringer – Worksheet p.

PROVE STATEMENTS ABOUT SEGMENTS & ANGLES. EXAMPLE 1 Write a two-column proof Write a two-column proof for the situation in Example 4 on page 107. GIVEN:

Algebraic proof Chapter 2 Section 6.

Postulates and Algebraic Proofs Advanced Geometry Deductive Reasoning Lesson 2.

Vocabulary algebraic proof – Made up of algebraic statements two-column proof/formal proof – contains statements and reasons in two columns.

Lesson 2 – 6 Algebraic Proof

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) CCSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

UNIT 01 – LESSON 11 – ALGEBRAIC PROOFS ESSENTIAL QUESTION How can algebraic properties help you solve an equation? SCHOLARS WILL… Use algebra to write.

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.

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

2.5 Reason Using Properties from Algebra Objective: To use algebraic properties in logical arguments.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–6) CCSS Then/Now Postulate 2.8: Ruler Postulate Postulate 2.9: Segment Addition Postulate.

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.

Bell Ringer. Then/Now You used postulates about points, lines, and planes to write paragraph proofs. Use algebra to write two-column proofs. Use properties.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–5) CCSS Then/Now New Vocabulary Key Concept: Properties of Real Numbers Example 1:Justify.

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,

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

Algebraic Proof LESSON 2–6. Lesson Menu Five-Minute Check (over Lesson 2–5) TEKS Then/Now New Vocabulary Key Concept: Properties of Real Numbers Example.

USING PROPERTIES FROM ALGEBRA ALGEBRAIC PROPERTIES OF EQUALITY Let a, b, and c be real numbers. SUBTRACTION PROPERTY ADDITION PROPERTY If a = b, then a.

2-6 Prove Statements About Segments and Angles Hubarth Geometry.

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

Concept. Example 1 Identifying Postulates ARCHITECTURE Explain how the picture illustrates that the statement is true. Then state the postulate that.

A. A line contains at least two points.

5.2 Notes: Algebraic Proof

Chapter 2.6 Algebraic Proof.

Five-Minute Check (over Lesson 2–4) Mathematical Practices Then/Now

Five-Minute Check (over Lesson 2–3) Mathematical Practices Then/Now

Proving Segment Relationships

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

1. SWBAT use algebra to write two column proofs

2.5 Reasoning in Algebra and Geometry

Write proofs involving supplementary and complementary angles.

Starter(s): Find one counterexample to show that each conjecture is false. All vehicles on the highway have exactly four wheels. 2. All states in the United.

Use algebra to write two-column proofs.

Identify and use basic postulates about points, lines, and planes.

If an organism is a parasite, then it survives by living on or in a host organism. If a parasite lives in or on a host organism, then it harms its.

Prove Statements about Segments and Angles

LESSON 2–6 Algebraic Proof.

Day 5 – Introduction to Proofs

Reasoning with Properties from Algebra

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

Five-Minute Check (over Lesson 2–6) Mathematical Practices Then/Now

Five-Minute Check (over Lesson 2–4) Mathematical Practices Then/Now

Five-Minute Check (over Lesson 2–3) Mathematical Practices Then/Now

Proving Statements about Segments

Presentation transcript:

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 that A, B, and C are collinear? Define: Algebraic Proof BellRinger

CCSS Content Standards Preparation for G.CO.9 Prove theorems about lines and angles. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others.

Then/Now You used postulates about points, lines, and planes to write paragraph proofs. Use algebra to write two-column proofs. Use properties of equality to write geometric proofs.

Concept

Example 1 Justify Each Step When Solving an Equation Solve 2(5 – 3a) – 4(a + 7) = 92. Algebraic StepsProperties 2(5 – 3a) – 4(a + 7)=92Original equation 10 – 6a – 4a – 28=92Distributive Property –18 – 10a=92Substitution Property –18 – 10a + 18 = Addition Property

Example 1 Justify Each Step When Solving an Equation Answer: a = –11 –10a=110Substitution Property Division Property a=–11Substitution Property

Example 1 A.a = 12 B.a = –37 C.a = –7 D.a = 7 Solve –3(a + 3) + 5(3 – a) = –50.

Example 2 Write an Algebraic Proof Begin by stating what is given and what you are to prove.

Example 2 Write an Algebraic Proof 2. d – 5 = 20t2. Addition Property of Equality StatementsReasons Proof: 1. Given 1. d = 20t Symmetric Property of Equality 3.3. Division Property of Equality = t

Example 2 Which of the following statements would complete the proof of this conjecture? If the formula for the area of a trapezoid is, then the height h of the trapezoid is given by.

Example 2 StatementsReasons Proof: 3.3. Division Property of Equality 4.4. Symmetric Property of Equality 1. Given 1. 2._____________2. Multiplication Property of Equality ?

Example 2 A.2A = (b 1 + b 2 )h B. C. D.

Groupwork: P139 #1-5 Homework: Worksheet 2-6

Example 3 Write a Geometric Proof If  A  B, m  B = 2m  C, and m  C = 45, then m  A = 90. Write a two-column proof to verify this conjecture.

Example 3 5. m  A = Substitution StatementsReasons Proof: 4. Substitution 4. m  A = 2(45) Write a Geometric Proof 2. m  A = m  B 2. Definition of angles 1. Given 1.  A  B; m  B = 2m  C; m  C = Transitive Property of Equality 3. m  A = 2m  C

Example 3

StatementsReasons Proof: 1. Given _______________ ? 3. AB = RS3. Definition of congruent segments 4. AB = 124. Given 5. RS = 125. Substitution

Example 3 A. Reflexive Property of Equality B. Symmetric Property of Equality C.Transitive Property of Equality D. Substitution Property of Equality

End of the Lesson