proving segment relationships

Proving Segment Proving Segment RelationshipsRelationships

• Write proofs involving segment addition.

• Write proofs involving segment congruence.

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

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.

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

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

Prove the following.

Given: AC = ABAB = BXCY = XD

Prove: AY = BD

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

Proof with Segment Congruence

Prove the following.

Given:

Prove:

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

Prove the following.

Given:

Prove:

Which choice correctly completes the proof?

Proof:Statements Reasons

1. Given1.

2. Transitive Property2.

3. Given3.

4. Transitive Property4.

5. _______________5. ?Symmetric Property

HomeworkHomework

Chapter 2-7Chapter 2-7

• Pg 121Pg 121

1 – 3, 16, 19 – 291 – 3, 16, 19 – 29