Splash Screen.

Slides:

Advertisements

Similar presentations

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

Advertisements

Reflexive example: AB = AB Symmetric example: AB = BA

Proving Segment Relationships

Over Lesson 2–6 5-Minute Check 1 A.Distributive Property B.Addition Property C.Substitution Property D.Multiplication Property State the property that.

Verifying Segment Relations

Proving Segment Relationships

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

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

Chapter 2 Properties from Algebra

4.5 Segment and Angle Proofs

2-7 Proving Segment Relationships You wrote algebraic and two-column proofs. Write proofs involving segment addition. Write proofs involving segment congruence.

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:

Bell Ringer 03 Discussion on Midterm and Quiz You are required to go to at least 2 days of tutoring for test corrections if you have A score of 13 (68%)

Algebraic proof Chapter 2 Section 6.

Building a System of Geometry Knowledge 2.4

2.4: Building a System of Geometric Knowledge

BELL RINGER PROBLEM State the property that justifies the statement. If BC = CD and CD = EF, then BC = EF. A. Reflexive Property B. Symmetric Property.

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

Section 2.4: Reasoning in Algebra

2.5 Proving Statements and Segments. Properties of Segment Congruence Segment congruence is reflexive, symmetric, and transitive. Reflexive: For any segment.

Lesson: 15 – 4 Preparing for Two-Column Proofs

Lesson 7 Menu Warm-up Problems State the property that justifies each statement. 1.2(LM + NO) = 2LM + 2NO. 2.If m  R = m  S, then m  R + m  T = m 

 ESSENTIAL QUESTION  How can you prove a mathematical statement?  Scholars will..  Write proofs involving segment addition.  Write proofs involving.

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

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.

Splash Screen. Over Lesson 2–6 5-Minute Check 1 A.Distributive Property B.Addition Property C.Substitution Property D.Multiplication Property State the.

2.5 Reasoning and Algebra. Addition Property If A = B then A + C = B + C.

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.

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

Proving Statements about Segments

Lesson 2 – 7 Proving Segment Relationships

definition of a midpoint

Using Segment and Angle Addition Postulates

Reasoning in Algebra and Geometry

Write a two-column proof

Warm Up Rewrite each term using math symbols you learned in chapter 1 (symbols for a line, angle, ray, etc.) Example: MN Ray MN _________________________________________________________.

2.4 Objective: The student will be able to:

Chapter 2.6 Algebraic Proof.

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

Proving Statements about Segments

Proving Segment Relationships

4.5 Segment and Angle Proofs

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

2.3 Proving Theorems Midpoint & Angle Bisector Theorem

2-5 Reason Using Properties from Algebra

Unit 1 Day 10 TWO COLUMN PROOFS.

1. SWBAT use algebra to write two column proofs

2. Definition of congruent segments AB = CD 2.

Proving Segment Relationships

2.5 Proving Statements about Segments

Use the properties of Real Numbers to justify each step when solving the following equation:

Prove Statements about Segments and Angles

a + c = b + c a - c = b - c ac = bc a c b = a can be

Lesson 2-5: Algebraic Proofs

Put CW/HW on the corner of your desk!

2.7 Proving Segment Relationships

2-6 Prove Statements About Segments and Angles

2.7 Proving Statements about Segments

Verifying Segment Relationships

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

4.5 Segment and Angle Proofs

Presentation transcript:

Splash Screen

You wrote algebraic and two-column proofs. (Lesson 2–6) Write proofs involving segment addition. Write proofs involving segment congruence. Then/Now

Concept

Concept

2. Definition of congruent segments AB = CD 2. Use the Segment Addition Postulate Proof: Statements Reasons 1. 1. Given AB  CD ___ 2. Definition of congruent segments AB = CD 2. 3. Reflexive Property of Equality BC = BC 3. 4. Segment Addition Postulate AB + BC = AC 4. Example 1

5. Substitution Property of Equality 5. CD + BC = AC Use the Segment Addition Postulate Proof: Statements Reasons 5. Substitution Property of Equality 5. CD + BC = AC 6. Segment Addition Postulate CD + BC = BD 6. 7. Transitive Property of Equality AC = BD 7. 8. Definition of congruent segments 8. AC  BD ___ Example 1

Given: AC = AB AB = BX CY = XD Prove the following. Given: AC = AB AB = BX CY = XD Prove: AY = BD Example 1

Which reason correctly completes the proof? 1. Given AC = AB, AB = BX 1. 2. Transitive Property AC = BX 2. 3. Given CY = XD 3. 4. Addition Property AC + CY = BX + XD 4. AY = BD 6. Substitution 6. Proof: Statements Reasons Which reason correctly completes the proof? 5. ________________ AC + CY = AY; BX + XD = BD 5. ? Example 1

A B C D A. Addition Property B. Substitution C. Definition of congruent segments D. Segment Addition Postulate A B C D Example 1

Concept

Concept

Proof Using Segment Congruence BADGE Jamie is designing a badge for her club. The length of the top edge of the badge is equal to the length of the left edge of the badge. The top edge of the badge is congruent to the right edge of the badge, and the right edge of the badge is congruent to the bottom edge of the badge. Prove that the bottom edge of the badge is congruent to the left edge of the badge. Given: Prove: Example 2

2. Definition of congruent segments 2. Proof Using Segment Congruence Proof: Statements Reasons 1. Given 1. 2. Definition of congruent segments 2. 3. Given 3. 4. Transitive Property 4. YZ ___ 5. Substitution 5. Example 2

Prove the following. Given: Prove: Example 2

Which choice correctly completes the proof? Proof: Statements Reasons 1. Given 1. 2. Transitive Property 2. 3. Given 3. 4. Transitive Property 4. 5. _______________ 5. ? Example 2

A B C D A. Substitution B. Symmetric Property C. Segment Addition Postulate D. Reflexive Property A B C D Example 2

End of the Lesson