Final answer:
The substitution property of equality is used to replace BC with AB when AB is equal to BC, giving us AB + AB = AC. The commutative property of addition also applies, as the order in which two numbers are added doesn't affect their sum.
Step-by-step explanation:
The property that allows AB + BC = AC to become AB + AB = AC when AB = BC is known as the substitution property of equality. This means if two quantities are equal, one can be substituted for the other in any equation or expression. Since AB is equal to BC, we substitute BC with AB to get AB + AB = AC.
The commutative property of addition, which states A+B = B+A, is also relevant as it implies that the order in which numbers are added does not change the sum. This principle is also true for the addition of vectors and other mathematical entities.