Final answer:
The statement regarding the trapezoids' side lengths is false due to a typographical error and the requirement for similarity that all sides be proportional, which cannot be confirmed without additional information.
Step-by-step explanation:
The statement 'The length of each side of trapezoid PQRS is 3 times the length of its corresponding side of trapezoid ABCD' is false.
In the given scenario, there is a typographical error as the trapezoid mentioned should be ACD instead of ABCD. Assuming that 'ACD' is the correct trapezoid, if trapezoid ACD is similar to trapezoid PQRS, then the corresponding sides of the trapezoids should be proportional.
Because they are similar, if one side of PQRS is three times its corresponding side in ACD, then all sides of PQRS must also be three times the length of their corresponding sides in ACD. Without this consistent scaling factor, the trapezoids would not be similar.
However, to verify the similarity and the ratio of their corresponding sides, more geometric information is required, such as the lengths of the sides or angles of the trapezoids.
If trapezoid ACD is similar to trapezoid PQRS, it means that their corresponding angles are equal. However, in the statement given, it is stated that the length of each side of trapezoid PQRS is 3 times the length of its corresponding side of trapezoid ACD. This implies that the sides are not proportional, which contradicts the definition of similar trapezoids. Therefore, the statement is false.