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

Postulate 2.8: Ruler Postulate Postulate 2.9: Segment Addition Postulate Example 1: Use the Segment Addition Postulate Theorem 2.2: Properties of Segment Congruence Proof: Transitive Property of Congruence Example 2: Real-World Example: Proof Using Segment Congruence Lesson Menu

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**State the property that justifies the statement. 2(LM + NO) = 2LM + 2NO**

A. Distributive Property B. Addition Property C. Substitution Property D. Multiplication Property A B C D 5-Minute Check 1

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**State the property that justifies the statement**

State the property that justifies the statement. If mR = mS, then mR + mT = mS + mT. A. Distributive Property B. Substitution Property C. Addition Property D. Transitive Property A B C D 5-Minute Check 2

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**State the property that justifies the statement. If 2PQ = OQ, then PQ =**

A. Multiplication Property B. Division Property C. Distributive Property D. Substitution Property A B C D 5-Minute Check 3

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**A B C D State the property that justifies the statement. mZ = mZ**

A. Reflexive Property B. Symmetric Property C. Transitive Property D. Substitution Property A B C D 5-Minute Check 4

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**State the property that justifies the statement**

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 A B C D 5-Minute Check 5

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**A B C D Which statement shows an example of the Symmetric Property?**

A. x = x B. If x = 3, then x + 4 = 7. C. If x = 3, then 3 = x. D. If x = 3 and x = y, then y = 3. A B C D 5-Minute Check 6

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**You wrote algebraic and two-column proofs. (Lesson 2–6)**

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

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Concept

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Concept

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**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

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**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

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**Given: AC = AB AB = BX CY = XD**

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

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**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

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**A B C D A. Addition Property B. Substitution**

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

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Concept

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Concept

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**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

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**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

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Prove the following. Given: Prove: Example 2

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**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

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**A B C D A. Substitution B. Symmetric Property**

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

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End of the Lesson

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Proving Segment Relationships Postulate 2.8 - The Ruler Postulate The points on any line or line segment can be paired with real numbers so that, given.

Proving Segment Relationships Postulate 2.8 - The Ruler Postulate The points on any line or line segment can be paired with real numbers so that, given.

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