1. Given: ADE, AOC, BOD are straight lines; OA = OC; OB = OD; AD = DE. 2. Triangles OAB and OCD are congruent by SAS since OA = OC, OB = OD, and angles AOC and BOD are equal. 3. From congruence, BC = ED. 4. Since AD = DE and points A, D, E are collinear, DE is parallel and equal to AD. 5. DE is parallel to AB, and BC is parallel to AD by congruence and equal lengths. 6. Therefore, BC = ED and BC is parallel to ED. 7. Using congruent triangles and given equalities, BE = CD and BE is parallel to CD. 8. Both pairs of opposite sides BC and ED, and BE and CD are equal and parallel. 9. Hence, quadrilateral BCED is a parallelogram. Final answer: BCED is a parallelogram.