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2-5 Algebraic Proof
Vocabulary
Proof: an argument that uses logic, definitions,
properties, and previously proven statements to show
that a conclusion is true.
3 Aspects of Proof:
1. Starts with a given fact.
2. Is logical and organized.
3. Every step is justified (has a reason).
Example 1: Solving an Equation in Algebra
Solve the equation 4m – 8 = –12. Write a
justification for each step.
4m – 8 = –12
+8
+8
4m
= –4
Given equation
Addition Property of Equality
Simplify
Division Property of Equality
m = –1
Simplify
Example 2: Problem-Solving Application
What is the temperature in degrees Fahrenheit F
when it is 15°C? Solve the equation F =9 C + 32
5
for F and justify each step.
Given equation
Substitution Property of Equality
F = 27 + 32
F = 59
F = 59°
Simplify.
Simplify.
Example 3: Solving an Equation in Geometry
Solve for x. Write a justification for each step.
NO = NM + MO
Segment Addition Post.
4x – 4 = 2x + (3x – 9) Substitution Prop. of Equality
4x – 4 = 5x – 9
–4 = x – 9
5=x
Simplify
Subtraction Prop. of Equality
Addition Prop. of Equality
Example 4: Identifying Property of Equality and
Congruence
Identify the property that justifies each
statement.
A. QRS  QRS
Reflex. Prop. of .
B. m1 = m2 so m2 = m1
Symm. Prop. of =
C. AB  CD and CD  EF, so AB  EF. Trans. Prop of 
D. 32° = 32°Reflex. Prop. of =