Answer:
Statements Reasons
AC+CD=AD and AB+BD=AD Segment Addition Postulate
AC+CD=AB+BD Transitive/Substitution Property
AC=BD Given
BD+CD=AB+BD Substitution Property
CD=AB Subtraction Property
AB=CD Symmetric Property
Explanation:
By segment addition postulate, we can say the following two equations:
AC+CD=AD and AB+BD=AD.
By either substitution/transitive property, you can say AC+CD=AB+BD.
You are given AC=BD, so we use substitution and write AC+CD=AB+AC.
After using subtraction property (subtracting both sides by AC), you obtain CD=AB.
By symmetric property, you may say AB=CD.
So let's write it into the 2 column-proof you have there:
Statements Reasons
AC+CD=AD and AB+BD=AD Segment Addition Postulate
AC+CD=AB+BD Transitive/Substitution Property
AC=BD Given
BD+CD=AB+BD Substitution Property
CD=AB Subtraction Property
AB=CD Symmetric Property
Properties/Postulates used:
Transitive property which says:
If a=b and b=c, then a=c.
Substitution property which says:
If a=b, then b can be substituted(replaced with) for a.
Subtraction property which says:
a=b implies a-c=b-c.
Segment Addition Postulate says:
If you break a segment into two smaller pieces then the measurement of that segment is equal to the sum of the smaller two segments' measurements.