This proposition is a converse of the previous one, stating that if two adjacent angles sum to two right angles, then they must lie in a line. Like many converse theorems, this one is proven by contradiction. It's assumed that BD does not lie in a line with CB, meaning it's possible to construct a line BE that does lie in a line with CB. This allows Euclid to use the previous theorem. This line of logic of assuming something does not have the desired property, then using that to construct something that does have the desired property, is a common tactic for proof. Once BE is constructed, it's easy to see why angle ABD equals angle ABE, and Euclid would call this, "the lesser equals the greater"; a contradiction.