Proving Segment Relationships

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Proving Segment Proving Segment Relationships Relationships

description

Proving Segment Relationships. Write proofs involving segment addition. Write proofs involving segment congruence. Standard 4.0 Students prove basic theorems involving congruence and similarity. (Key). Lesson 7 MI/Vocab. AC. A. B. C. 5. 8. AB. BC. Segment Addition Postulate. - PowerPoint PPT Presentation

Transcript of Proving Segment Relationships

Page 1: Proving Segment Relationships

Proving Segment Proving Segment RelationshipsRelationships

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• Write proofs involving segment addition.

• Write proofs involving segment congruence.

Standard 4.0 Students prove basic theorems involving congruence and similarity. (Key)

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Segment Addition Postulate

• If B is b/t A and C, then AB + BC = AC.

• If AB + BC = AC, then B is b/t A and C.

A B CAC

AB BC5 8

13

If AB = 5 and BC = 8, then AC = 5 + 8 = 13.

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Segment Addition Postulate

If AB = 3x + 2

BC = 5x – 3

AC = 15

Solve for x.

A B C

AB + BC = AC

(3x + 2) + (5x – 3) = 15

8x –1 = 15

8x = 16

x = 2

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Proof with Segment Addition

1. GivenPR = QS1.

2. Subtraction PropertyPR – QR = QS – QR2.

3. Segment Addition Postulate

PR – QR = PQ; QS – QR = RS

3.

4. SubstitutionPQ = RS4.

Proof:Statements Reasons

Prove the following.

Given: PR = QSProve: PQ = RS

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Prove the following.

Given: AC = ABAB = BXCY = XD

Prove: AY = BD

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1. GivenAC = AB, AB = BX1.

2. Transitive PropertyAC = BX2.

3. GivenCY = XD3.

4. Addition PropertyAC + CY = BX + XD4.

AY = BD 6. Substitution6.

Proof:Statements Reasons

Which choice correctly completes the proof?

5. ________________AC + CY = AY; BX + XD = BD

5. ?Segment Addition

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Proof with Segment Congruence

Prove the following.

Given:

Prove:

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5. Symmetric Property5.

Proof:Statements Reasons

1. Given1.

2. Definition of congruent segments

2.

3. Given3.

4. Transitive Property4.

Prove:Given:

Proof with Segment Congruence

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Prove the following.

Given:

Prove:

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Which choice correctly completes the proof?

Proof:Statements Reasons

1. Given1.

2. Transitive Property2.

3. Given3.

4. Transitive Property4.

5. _______________5. ?Symmetric Property

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HomeworkHomework

Chapter 2-7Chapter 2-7

• Pg 121Pg 121

1 – 3, 16, 19 – 291 – 3, 16, 19 – 29