Download 2.5 Postulates and Paragraph Proofs

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Theorem and Proof
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A theorem is a statement or conjecture that has
been shown to be true.
Theorems can be used like a definition or
postulate to justify other statements are true.
A proof is a logical argument in which each
statement made is supported by a statement
that is accepted as true.
A paragraph proof or informal proof is one
type of proof.
2.5 Algebraic Proof
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Algebraic proofs use algebra to write twocolumn proofs.
Two-Column Proofs or formal proofs contains
statements and reasons organized into 2
columns.
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Each step is called a statement and the properties
that justify each step are called the reasons.
Properties of Equality for Real
Numbers
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Reflexive Property: a = a
Symmetric Property: if a = b, then b = a
Transitive Property: if a=b, and b=c, then a=c
Addition Property: if a=b, then a+c = b+c
Subtraction Property: if a=b, then a-c = b-c
Multiplication/Division: if a=b, then ac = bc
Substitution Property: if a=b, then a may be
replaced by b in any equation or expression
Distributive Property: a(b+c) = ab + ac
Example
Complete the following proof.
Given: 5- ½ x = 1
Prove: 8 = x
Statements
1.
5–½x=1
2.
5–½x–5=1–5
3.
- ½ x = -4
4.
_______________
5.
x=8
6.
8=x
Reasons
1. Given
2. ____________
3. ____________
4. Multiplication
5. _____________
6. _____________
Answer
Complete the following proof.
Given: 5- ½ x = 1
Prove: 8 = x
Statements
1.
5–½x=1
2.
5–½x–5=1–5
3.
- ½ x = -4
4.
-2( ½ x) = -2(-4)
5.
x=8
6.
8=x
Reasons
1. Given
2. Subtraction
3. Substitution
4. Multiplication
5. Substitution
6. Symmetric Prop.