Final Answer:
If AB = CD, then CD = AB is justified by the symmetric property of equality.
Step-by-step explanation:
The symmetric property of equality states that if a = b, then b = a. In the given statement, AB = CD, the symmetric property allows us to rearrange the order of the equality, leading to CD = AB. This property is fundamental in algebraic reasoning, allowing us to manipulate equations and express relationships between quantities in a more flexible manner.
In this context, when we say AB = CD, it means that the lengths AB and CD are equal. Applying the symmetric property simply allows us to state the equality in the reverse order without changing its truth. This property is crucial in mathematical proofs and reasoning, enabling mathematicians to simplify expressions and equations by rearranging terms while maintaining the validity of the statement.
In summary, the symmetric property of equality justifies the interchangeability of the order of equal quantities. So, if AB = CD, then CD = AB by the symmetric property. This principle is foundational in mathematics, providing a powerful tool for algebraic manipulations and logical deductions.