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%) or below on your Midterm Part 1 and/or A score of 6.5 (65%) or below on your Midterm (Part 2) and/or Chapter 1 Corrections are due by tomorrow.

8 minutes CONNECTIONS PROTOCOL REFLECTION OPPORTUNITY Do Not Write on the Handout A way for you to build a bridge from where you are (mentally, physically), to where you are going and what you will be doing.

Bell Ringer (in your notes) You may use your notes on 2-7 only. Take out both postulate sheets 1.What is the title of Lesson 2-7? 2.What is the difference between a postulate and a theorem? 3.Explain the Segment Addition Postulate. 4.What are the Three Properties of Segment Congruence? When you are finished, take out your book and postulate sheet.

SAVE THE LAST WORD FOR ME PROTOCOL Article - The General Importance of Logic and Reasoning in Our Daily Lives Choose a timekeeper and a facilitator. You will have 10 minutes to read the article.

Enduring Understandings: What should I know 20 years from now? 1. A problem solver understands what has been done, knows why the process was appropriate, and can support it with reasons and evidence. 2. Logical reasoning will help us make wise decision when faced with a given situation Essential Questions 1. How will proofs enhance our logical reasoning skills? 2. How and where do I begin to start solving a problem?

CCSS Content Standards G.CO.9 Prove theorems about lines and angles. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Mathematical Practices 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others.

Then/Now Write proofs involving segment addition. Write proofs involving segment congruence.

Concept

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

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

Example 1 Prove the following. Given:AC = AB AB = BX CY = XD Prove:AY = BD Write the given and prove statement above, and then draw the figure.

Example 1 1. Given AC = AB, AB = BX Transitive Property AC = BX Given CY = XD Addition PropertyAC + CY = BX + XD4. AY = BD 6. Substitution6. Proof: StatementsReasons Which reason correctly completes the proof? 5. ________________ AC + CY = AY; BX + XD = BD 5. ?

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

Concept

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

Example 2 Prove the following. Given: Prove:

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

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

Class Assignment p , 4