Page 193 - Math Course 2 (Book 2)

Two-Column Algebraic Proof
Mo. 12

Lesson 6 formal proof

contains statements and reasons organized in two
columns used to prove conjectures and theorems.

KEY CONCEPTS: Write a two-column proof to show that if 3(x – )= 1,
5
then x = 2. 3
1. Use algebra to write two-column proofs. Statements Reasons
2. Use properties of equality in geometry 5
proofs. 1. 3 (x – ) = 1 1. Given
3
5
2. 3x – 3( )= 1 2. Distributive Property
3
3. 3x – 5 = 1 3. Substitution
MO. 12 - L6a
4. 3x – 5 + 5 = 1 + 5 4. Addition Property
Use Algebra to Write 5. 3x = 6 5. Substitution

Two-Column Proofs 3x 6
6. =
3 3 6. Division Property
7. x = 2 7. Substitution
Vocabulary A-Z

Let us learn some vocabulary
Key Concept

deductive argument
A group of algebraic steps used to solve problems The following properties are true for any numbers
form a deductive argument. a, b, and c.

Algebraic Steps Properties Reflexive Property a = a

3(x – 2) = 42 Original Equation
3x – 6 = 42 Distributive Property Symmetric Property If a = b, then b = a
3x – 6 + 6 = 42 + 6 Addition Property
3x = 48 Substitution Property Transitive Property If a = b and b = c, then
3x 48 a = c
= 3 Division Property
3
x = 16 Substitution Property Addition and If a = b, then a + c = b + c
Subtraction
and a – c = b – c.
two-column proof Properties
contains statements and reasons organized in two Multiplication and If a = b, then a • c = b and
columns used to prove conjectures and theorems. Division Properties if c ≠ 0, = b
a
5
Write a two-column proof to show that if 3(x – )= 1, c c
3
then x = 2. Substitution If a = b, then a may be
Statements Reasons replaced by b in any
5 Property equation or expression.
1. 3 (x – ) = 1 1. Given
3 Distributive
5
2. 3x – 3( )= 1 2. Distributive Property a(b + c) = ab + ac.
3 Property
3. 3x – 5 = 1 3. Substitution
4. 3x – 5 + 5 = 1 + 5 4. Addition Property

5. 3x = 6 5. Substitution
3x
6. = 6 6. Division Property
3 3
7. x = 2 7. Substitution
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