Cho BC = 2AB, A = 60°. Tứ giác ABFE? Tứ giác AIEF? Tứ giác BICD?

To analyze the quadrilaterals and triangles based on the given conditions in your geometry problem, we can proceed as follows:

### Given:

1. \( BC = 2AB \)
2. \( \angle A = 60^\circ \)

### Questions:

a) **Tứ giác ABFE (Quadrilateral ABFE)**:

To determine if ABFE is a specific type of quadrilateral, we should look at the sides and angles.

- Since \( BC \) is twice \( AB \), and all sides are marked with parallel lines, we may check for properties related to parallelism and similarity.

b) **Tứ giác AIEF (Quadrilateral AIEF)**:

- This quadrilateral will also need analysis based on external angles and side lengths. Given the properties of the other shapes and lengths, we can deduce relationships.

c) **Tứ giác BICD (Quadrilateral BICD)**:

- This quadrilateral may utilize the properties of the other triangles and the angles given. Again, parallelogram or trapezoidal properties may help in concluding the type.

d) **AED**:

For triangle AED, we can check for special angles, side lengths, and properties like Isosceles or Equilateral, depending on the given sides.

### Conclusion

For each of these quadrilaterals or triangles, we can classify them based on the relationships defined by the sides and angles. You may be looking for specific classifications such as:

- **Parallelograms**: If opposite sides are equal and parallel.
- **Trapezoids**: If only one pair of sides is parallel.
- **Triangles**: Classify based on side lengths or angle measures.

To fully classify each shape accurately, we’d apply properties of parallelism, angle relationships, and the given side lengths, all taking into account the \( 60^\circ \) angle given. If you need specific classifications or further deductions on properties, please specify!