Properties for real numbers a, b, and c

• Addition- If a=b, then a+c=b+c
• Subtraction- If a=b, then a-c=b-c
• Multiplication- If a=b, then ac=bc
• Division- If a=b, then a/c=b/c
• Reflexive- a=a
• Symmetric- If a=b, then b=a
• Transitive- If a=b and b=c, then a=c
• Substitution- If a=b, then b can replace a
• Distributive- a(b+c)=ab+ac
• Also recall angle addition postulate and segment addition postulate.

That may seem like alot, but many of these are common sense and very simple. You use these properties and postulates to explain (justify) your algebraic steps.

Example

Given: Line LM bisects 

Line LM bisects GIVEN

mDEFINITION OF ANGLE BISECTOR

4x=2x+40 – SUBSTITUTION PROPERTY

2x=40 – SUBTRACTION PROPERTY

x=20 – DIVISION PROPERTY

Further Reading

• Geometry Help: Deductive Reasoning
• Geometry Help: Biconditionals and Definitions