Download - 2-6 Algebraic Proof p. 136
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2-6 Algebraic Proofp. 136
You used postulates about points, lines, and planes to write paragraph proofs.
•Use algebra to write two-column proofs.
•Use properties of equality to write geometric proofs.
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Proofs
A proof is a logical argument in which each statement you make is supported by a statement that is accepted as true.It can be written as:A paragraphTwo column or formalFlow chart.
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Page 136
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Algebraic Proofs
You just saw a table summarizing the properties of real numbers you studied in Algebra.Now you will use these properties in Algebraic Proofs.An algebraic proof is a proof that is made up of a series of algebraic statements.
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Solve 2(5 – 3a) – 4(a + 7) = 92.Algebraic Steps Properties
2(5 – 3a) – 4(a + 7) = 92 Original equation
10 – 6a – 4a – 28 = 92 Distributive Property
–18 – 10a = 92 Substitution Property
–18 – 10a + 18 = 92 + 18 Addition Property
Justify Each Step When Solving an Equation
Answer: a = –11
–10a = 110 Substitution Property Division Property
a = –11 Substitution Property
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A. a = 12
B. a = –37
C. a = –7
D. a = 7
Solve –3(a + 3) + 5(3 – a) = –50.
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Begin by stating what is given and what you are to prove.
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2. d – 5 = 20t 2. Addition Property of Equality
Statements ReasonsProof:
1. Given 1. d = 20t + 5
4. 4. Symmetric Property of Equality
3. 3. Division Property of Equality= t
*Hint* always start with GIVENAlways end with PROVE
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Which of the following statements would complete the proof of this conjecture?
If the formula for the area of a trapezoid is
, then the height h of the trapezoid is
given by .
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Statements ReasonsProof:
3. 3. Division Property of Equality
4. 4. Symmetric Property of Equality
1. Given1.
2._____________
2. Multiplication Property of Equality
?2A = (b1 + b2)h
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If A B, mB = 2mC, and mC = 45, then mA = 90. Write a two-column proof to verify this conjecture.
5. mA = 90 5. Substitution
Statements ReasonsProof:
4. Substitution4. mA = 2(45)
2. mA = mB 2. Definition of angles
1. Given1. A B; mB = 2mC; mC = 45
3. Transitive Property of Equality
3. mA = 2mC
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Statements ReasonsProof:
1. Given1.
2. 2. _______________?
3. AB = RS 3. Definition of congruent segments
4. AB = 12 4. Given
5. RS = 12 5. Substitution
Transitive Property of Equality
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2-6 Assignment
Page 139, 2-16 even, 17, 18Write out all of the information in the book for
17 & 18That includes:
GivenProve
StatementsReasons