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Warm-up Problems State the property that justifies each statement. 2( LM + NO ) = 2 LM + 2 NO . If m R = m S , then m R + m T = m S + m T . m Z = m Z . If BC = CD and CD = EF , then BC = EF . - PowerPoint PPT PresentationTRANSCRIPT
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.
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
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
Proof with Segment Congruence
5. Symmetric Property5.
Proof:Statements Reasons
1. Given1.
2. Definition of congruent segments
2.
3. Given3.
4. Transitive Property4.
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