Final answer:
In a parallelogram, opposite sides are equal, so when taking the ratios of opposite sides, we find that AB/BC equals CD/AD because both ratios simplify to 1 using the property of division of equal numbers.
Step-by-step explanation:
To prove that in a parallelogram AB/BC = CD/AD, we start by stating that in parallelogram ABCD, the opposite sides are equal in length, that is, AB = CD and BC = AD. Therefore, the ratios AB/BC and CD/AD can be written as AB/AD and CD/BC, respectively.
Since AB = CD and BC = AD in a parallelogram, we have the ratios AB/AD = CD/CD and CD/BC = AB/AB. By the property that any number divided by itself is 1, these ratios simplify to 1, making AB/BC equal to CD/AD. Hence, we have proven the equality AB/BC = CD/AD by using the properties of a parallelogram and the property of division of equal numbers.