Properties of arithmetics

Reflective property A quantity is congruent (equal) to itself. a=a Symmetric property If a=b, then b=a. Transitive property If a=b and b=c, then a=c. Addition postulate If equal quantities are added to equal quantities, the sum are same Subtraction postulate If equal quantities are subtracted from equal quantities, the difference are equal. Multiplication postulate If equal quantities are multiplied by equal quantities, the products are equal. (also double of equal quantities are equal.) Division postulate If equal quantities are divided by equal none zero quantities, the quotients are equal. (also halves of equal quantities are equal.) Substitution postulate A quantity may be substituted for its equal in any expression. Partition postulate The whole is equal to some of its parts. Also between of points: AB+BC=AC. Angle addition postulate: m<ABC+ m<CBD=m<ABD