Warm-up Problems

State the property that justifies each statement.1. 2(LM + NO) = 2LM + 2NO.2. If mR = mS, then mR + mT = mS + mT.3. mZ = mZ.4. If BC = CD and CD = EF, then BC = EF.5. Which property justifies the statement: If 90 = mI, then

mI = 90?

• Write proofs involving segment addition.• Write proofs involving segment congruence.

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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

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. ?

A. AB. BC. CD. D

A. Addition Property

B. Substitution

C. Definition of congruent symbols

D. Segment Addition Postulate

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Proof with Segment Congruence

Prove the following.

Given:

Prove:

Proof with Segment Congruence

5. Symmetric Property5.

Proof:Statements Reasons

1. Given1.

2. Definition of congruent segments

2.

3. Given3.

4. Transitive Property4.

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. ?

1. A2. B3. C4. D

A. Substitution

B. Symmetric Property

C. Segment Addition Postulate

D. Reflexive Property