1. 2-5 Algebraic Proof

2. Vocabulary
Proof: an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true.

3. 3 Aspects of Proof: Starts with a given fact.
Is logical and organized.
Every step is justified (has a reason).

6. Example 1: Solving an Equation in Algebra
Solve the equation 4m – 8 = –12. Write a justification for each step.
4m – 8 = – Given equation
Addition Property of Equality
4m = –4 Simplify
Division Property of Equality
m = – Simplify

7. Example 2: Problem-Solving Application
What is the temperature in degrees Fahrenheit F when it is 15°C? Solve the equation F = C + 32 for F and justify each step.
9 5
Given equation
Substitution Property of Equality
F = Simplify.
F = Simplify.
F = 59°

8. 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
Simplify
–4 = x – 9
Subtraction Prop. of Equality
5 = x
Addition Prop. of Equality

10. Example 4: Identifying Property of Equality and Congruence
Identify the property that justifies each statement.
A. QRS  QRS
B. m1 = m2 so m2 = m1
C. AB  CD and CD  EF, so AB  EF.
D. 32° = 32°
Reflex. Prop. of .
Symm. Prop. of =
Trans. Prop of 
Reflex. Prop. of =