I have an easy way to remember the reflex, symmetric and transitive properties of equality.

When thinking of reflexive, think of the word "reflection".  When you see your reflection, you see yourself. So reflexive would be something along the lines of "a = a" or "b = b".

When thinking of symmetric, think of the word "symmetry".  If you cut something in half and have two equal parts, the object is symmetrical about the cut.

In geometry this is like saying "a = b, then b = a".

The transitive property involves 3 things, notice "trans" meaning three, is part of transitive.

In geometry this is like saying "if a = b and b = c, then a = c"