Final answer:
To prove ABCD is a parallelogram, one must show opposite sides are parallel or equal. ABCD is already an isosceles trapezoid with parallel sides AC and BD, and DE congruent to DC indicates AB is also parallel and equal to CD.
Step-by-step explanation:
The question pertains to proving that a given isosceles trapezoid ABCD, with AC parallel to BD and DE congruent to DC, is in fact a parallelogram. To demonstrate that ABCD is a parallelogram, one must establish either that both pairs of opposite sides are parallel or that one pair of opposite sides is both parallel and equal in length. In this case, since ABCD is an isosceles trapezoid, we already know one pair of opposite sides (AC and BD) is parallel. If DE is congruent to DC, then triangle DEC is isosceles, and since DE is an extension of AB, it would imply that AB is parallel and equal to CD. Now we have both pairs of opposite sides that are parallel, which fits the definition of a parallelogram. Therefore, ABCD must be a parallelogram.