To determine the number of lines of reflective symmetry and centers of rotational symmetry for the parallelogram shown:

1. Reflective Symmetry: Reflective symmetry occurs when a figure can be divided into two mirror-image halves. Parallelograms, in general, do not possess any lines of reflective symmetry unless they are special types like a rectangle. Since the given parallelogram is not a rectangle, it has 0 lines of reflective symmetry.

2. Rotational Symmetry: A shape has rotational symmetry if it can be rotated by a certain angle and still look the same. A parallelogram typically has rotational symmetry of order 2, meaning it looks the same after a 180-degree rotation. Therefore, the parallelogram has 1 center of rotational symmetry.

Conclusion:

The correct answer is (b) 0 lines of reflective symmetry and one center of rotational symmetry.

Would you like more details or have any questions?

Follow-up Questions:

1. What are the conditions for a shape to have reflective symmetry?
2. How is rotational symmetry different from reflective symmetry?
3. Can a parallelogram ever have reflective symmetry? If so, under what conditions?
4. What are some real-world examples of objects with rotational symmetry?
5. How does the order of rotational symmetry affect the angle of rotation?

Tip:

Always check for both reflection and rotation to fully understand the symmetry of a shape.