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.

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Presentation transcript:

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 C. Substitution Property D. Transitive Property You do not necessarily need to put this in your notes, but be prepared to give your answer and your reasoning behind why you chose your answer. 5-Minute Check 5

You wrote algebraic and two-column proofs. Write proofs involving segment addition. Write proofs involving segment congruence. Then/Now

Concept

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Concept

Concept

Concept

Reflexive Property of Equality Substitution Property of Equality Use the Segment Addition Postulate You will use each of the following (not necessarily in this order): Given Reflexive Property of Equality Substitution Property of Equality Transitive Property of Equality Definition of Congruent Segments (used twice) Segment Addition Postulate (used twice) Example 1

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

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

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

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

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

Remember: You have a QUIZ on Friday over 2-6 & 2-7 HW: (2-7) Worksheet Remember: You have a QUIZ on Friday over 2-6 & 2-7 Concept