Construct a quadrilateral which is not a parallelogram, in which a pair of opposite angles and a pair of opposite sides are equal.
1. **Consider a parallelogram ABED**:
   - Let \( \angle A = \angle E < 90^\circ \).
   - Let \( AB = DE = a \).

2. **Construct the circumcircle \( L \) of \( \triangle BDE \)**:
   - The circumcircle \( L \) passes through points \( B, D, \) and \( E \).

3. **Construct a circle with center \( D \) and radius \( a \)**:
   - This circle intersects the circumcircle \( L \) at point \( C \neq E \).

4. **Verify the properties of quadrilateral \( ABCD \)**:
   - Since \( AB = DE = a \) and \( D \) is the center of the circle with radius \( a \), \( DC = a \).
   - Therefore, \( AB = DC \).
   - By construction, \( \angle A = \angle E \).

5. **Check if \( ABCD \) is a parallelogram**:
   - For \( ABCD \) to be a parallelogram, opposite sides must be equal and parallel.
   - Here, we only have \( AB = DC \) and \( \angle A = \angle E \), but no information about parallelism of opposite sides.

6. **Conclusion**:
   - Quadrilateral \( ABCD \) has a pair of opposite sides equal (\( AB = DC \)) and a pair of opposite angles equal (\( \angle A = \angle E \)).
   - However, it is not necessarily a parallelogram since the opposite sides are not guaranteed to be parallel.

The final answer is \( \boxed{ ABCD } \) is a quadrilateral with a pair of opposite sides and a pair of opposite angles equal, but it is not a parallelogram.