In a quadrilateral PQRS, `bar(PQ)||bar(RS)` and PR=QS. PQRS is a /an_____

Options

A. square
B. rectangle
C. rhombus
D. isosceles trapezium.

Explanation

To determine the type of quadrilateral PQRS given that \( \overline{PQ} \parallel \overline{RS} \) and \( PR = QS \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Properties of the Quadrilateral**:
- We have a quadrilateral PQRS.
- It is given that \( \overline{PQ} \parallel \overline{RS} \). This means that these two sides are parallel to each other.

2. **Analyze the Lengths of the Diagonals**:
- The problem states that \( PR = QS \). This indicates that the lengths of the diagonals PR and QS are equal.

3. **Determine the Type of Quadrilateral**:
- A quadrilateral with one pair of parallel sides is known as a trapezium (or trapezoid in some regions).
- Additionally, if the non-parallel sides (in this case, PR and QS) are equal in length, then the trapezium is specifically classified as an isosceles trapezium.

4. **Conclusion**:
- Since \( \overline{PQ} \parallel \overline{RS} \) and \( PR = QS \), we conclude that quadrilateral PQRS is an **isosceles trapezium**.

### Final Answer:
PQRS is an **isosceles trapezium**.