1. Let's start by defining the shapes: a trapezoid is a quadrilateral with at least one pair of parallel sides, and a parallelogram is a quadrilateral with two pairs of parallel sides. 2. Congruent trapezoids are trapezoids that have exactly the same size and shape, meaning all corresponding sides and angles are equal. 3. Parallelograms have opposite sides that are equal and parallel, and opposite angles that are equal. 4. To prove two trapezoids are congruent, you can use criteria such as Side-Angle-Side (SAS) or Angle-Side-Angle (ASA) depending on the given information. 5. For parallelograms, properties like opposite sides being equal and parallel, and diagonals bisecting each other, help in solving problems. 6. If you have specific problems or need to find lengths, angles, or prove congruency, please provide the details so I can guide you step-by-step.