1. The problem involves understanding the relationship between the angles and sides of two parallelograms in a tiled pattern. 2. Key properties of parallelograms: - Opposite sides are equal in length. - Opposite angles are equal. - Adjacent angles are supplementary, meaning their measures add up to 180 degrees. 3. Given that four angles at any point sum to 360 degrees, and two of these angles are equal, the other two must sum to the remainder. 4. The acute angle of one parallelogram is equal to the obtuse angle of the other parallelogram, and also equal to its own consecutive obtuse angle. 5. From these angle relationships, it follows that the angles of one parallelogram are congruent to the corresponding angles of the other parallelogram. 6. Since corresponding angles are congruent and the sides are equal (longer and shorter sides match), the two parallelograms are congruent by the Angle-Side-Angle (ASA) criterion. Final conclusion: The two parallelograms in the tiled pattern are congruent because their corresponding sides and angles are equal.