**Reflexive Property:**For every number $a$, then $a=a$.

**Symmetric Property:**For all numbers $a$ and $b$ , if $a=b$ , then $b=a$ .

**Transitive Property:**If $a=b$ and $b=c$ , then $a=c$ .

**Substitution Property:**If $a=b$ , then $b$ can be substituted for $a$ in any equation.

**Addition Property:**If $a=b$ , then $a+c=b+c$ .

**Subtraction Property:**If $a=b$ , then $a?c=b?c$ .

**Multiplication Property:**If $a=b$ , then $a\cdot c=b\cdot c$ .

**Division Property:**If $a=b$ , then $\frac{a}{c}=\frac{b}{c}$ .

**Distribution Property:**$a(b+c)=ab+ac$

When you solve an equation, you will want to use to the two-column proof. For example, if you want to show that $x=1$ for the equation $2(x+1)+1=5$ , then it will look like this:

Statements |
Reasons |

$2(x+1)+1=5$ | Given |

$2x + 2 + 1 =5$ | Distributive Property |

$2x=2$ | Subtraction Property |

$x=1$ | Division Property |