**The addition Postulate:**

If a = b and c = d, then a + c = b + d

**The Partition Postulate:**

AB + BC = AC

These are two different concepts. Let's try a proof:

As you can see, in step 2, we added equal quantities to each other. This is Addition Postulate.

But in step 3, we added a part plus a part equals a whole so this is Partition.

Let's try another example:

Here we used the Subtraction Postulate: subtracting equal quantities from equal quantities.

In step 3, we had the whole minus a part equals a part. This is still Partition Postulate.