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

Slides:

Advertisements

Similar presentations

SWLT: Write proofs using geometric theorems and use properties of special pairs of angles.

Advertisements

Verifying Segment Relations

Proving Segment Relationships Postulate The Ruler Postulate The points on any line or line segment can be paired with real numbers so that, given.

2.6 Prove Statements About Segments and Angles

2.5 Proving Statements about Segments

Chapter 2 Properties from Algebra

4.5 Segment and Angle Proofs

2.6 Prove Statements about Segments and Angles Objectives: 1.To understand the role of proof in a deductive system 2.To write proofs using geometric theorems.

EXAMPLE 3 Use properties of equality

Proving Theorems 2-3.

Lesson 2.6 p. 109 Proving Statements about Angles Goal: to begin two-column proofs about congruent angles.

2-5 Postulates and Paragraph Proofs (p.89)

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.

Proving Segment Relationships

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:

EXAMPLE 3 Use properties of equality Prove this property of midpoints: If you know that M is the midpoint of AB,prove that AB is two times AM and AM is.

Identify the Property which supports each Conclusion.

Building a System of Geometry Knowledge 2.4

4.5 Segment and Angle Proofs. Basic geometry symbols you need to know Word(s)SymbolDefinition Point A Line AB Line Segment AB Ray Angle ABC Measure of.

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.

Some properties from algebra applied to geometry PropertySegmentsAngles Reflexive Symmetric Transitive PQ=QP m

Geometry 9/5/14 - Bellwork.

What is a Proof? Pg. 19 Types of Proof

Lesson: 15 – 4 Preparing for Two-Column Proofs

EXAMPLE 1 Write a two-column proof Write a two-column proof for the situation in Example 4 from Lesson 2.5. GIVEN: m  1 = m  3 PROVE: m 

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.

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

Chapter 2 Review Proofs in Algebra. Vocabulary Addition and Subtraction Properties Multiplication and Division Properties Substitution Property Commutative.

Write a two-column proof

Lesson 2.5 Proving Statements about Segments VOCABULARY A true statement that follows as a result of other true statements is called a theorem. A two-column.

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

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,

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.

Warm Up Lesson Presentation Lesson Quiz

+ DO NOW- Complete #1-5 on the proofs worksheet that you picked up from the back of the classroom.

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

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.

Section 2.6. A proof is a logical argument that shows a statement is true. The first proof format we will use is called a two- column proof. A two-column.

2. 6 Prove Statement about Segments and Angles 2

Have your homework out and be in your seat when the bell rings!

Lesson 2 – 7 Proving Segment Relationships

Geometry Organising is what you do before you do something, so that when you do it, it is not all mixed up. A.A. Milne Today: Over Proof Intro 2.5.

definition of a midpoint

Write a two-column proof

4.5 Segment and Angle Proofs

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

Chapter Notes: Properties and Algebraic Proofs

2.5 Proving Statements about Segments and Angles

2.5 Reasoning in Algebra and Geometry

2. Definition of congruent segments AB = CD 2.

2.5 Proving Statements about Segments

2.5 Proving Statements about Segments

A logical argument that shows a statement is true.

4.5 Segment and Angle Proofs

Prove Statements about Segments and Angles

Section 2-4: Reasoning in Algebra

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

Properties of Equality and Proving Segment & Angle Relationships

2.7 Proving Segment Relationships

2-6 Prove Statements About Segments and Angles

G6 - Deductive Reasoning

4.4 Prove Triangles Congruent by SAS and HL

2.7 Proving Statements about Segments

Verifying Segment Relationships

4.5 Segment and Angle Proofs

Chapter 2 Segments and Angles.

Presentation transcript:

2-6 Prove Statements About Segments and Angles Hubarth Geometry

A proof is a logical argument that shows a statement is true. We will use a two-column proof. A two column-proof has numbered statements and corresponding reasons for each step of the argument in logical order. Ex 1 Write a Two-Column Proof Write a two-column proof for the situation in Example 4 from Lesson 2.5. GIVEN: m ∠ 1 = m ∠ 3 PROVE: m ∠ EBA = m ∠ DBC 1. m ∠ 1 = m ∠ 3 2. m ∠ EBA = m ∠ 3 + m ∠ 2 3. m ∠ DBC = m ∠ 1 + m ∠ 2 1. Given 2. Angle Addition Postulate 3. Angle Addition Postulate STATEMENT REASONS 4. Substitution 5. m ∠ EBA = m ∠ DBC 5. Transitive Property of Equality

Theorems Congruence of Segments Segment congruence is reflexive, symmetric and transitive. Reflexive Symmetric Transitive Congruence of Angles Angle congruence is reflexive, symmetric and transitive Reflexive Symmetric Transitive

Name the property illustrated by the statement. a. Transitive Property of Angle Congruence b. Symmetric Property of Segment Congruence Ex 2 Name the Property Shown

Prove this property of midpoints: If you know that M is the midpoint of AB,prove that AB is two times AM and AM is one half of AB. GIVEN: M is the midpoint of AB. PROVE: a. AB = 2 AM b. AM = AB 2 1 Ex 3 Use Properties of Equality STATEMENT REASONS 1. M is the midpoint of AB. 2. AM MB 3. AM = MB 4. AM + MB = AB 1. Given 2. Definition of midpoint 3. Definition of congruent segments 4. Segment Addition Postulate 5.AM + AM = AB5. Substitution Property of Equality 6.2AM = AB a. AM = AB b. 6. Combine Like Terms 7. Division Property of Equality

Writing A Two-Column Proof Proof of the Symmetric Property of Angle Congruence Given: Prove: 12 StatementsReasons Given Def. of Congruent Angles Symmetric Property of Equality Definition of Congruent Angles

Practice GIVEN : AC = AB + AB PROVE : AB = BC 1. Four steps of a proof are shown. Give the reasons for the last two steps. 1. AC = AB + AB 2. AB + BC = AC 3. AB + AB = AB + BC 4. AB = BC 1. Given 2. Segment Addition Postulate 3. Transitive Property of Equality 4. Subtraction Property of Equality STATEMENT REASONS a. CD CD Reflexive Property of CongruenceSymmetric Property of Congruence 2. Name the property illustrated by the statement.