Which of the following statements are true (T) and which are false (F)? (i) In a parallelogram, the diagonals are equal. (ii) In a parallelogram, the diagonals bisect each other. (iii) In a parallelogram, the diagonals intersect each other at right angles. (iv) In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram. (v) If all the angles of a quadrilateral are equal, it is a parallelogram. (vi) If three sides of a quadrilateral are equal , it is a parallelogram. (vii) If three angles of a quadrilateral are equal, it is a parallelogram. (viii) If all the sides of a quadrilateral are equal it is a parallelogram

Explanation

To determine which statements about quadrilaterals are true (T) and which are false (F), we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement (i): In a parallelogram, the diagonals are equal.**
- **Analysis**: This statement is **False (F)**. In a general parallelogram, the diagonals are not necessarily equal. They are equal only in the special case of a rectangle.

2. **Statement (ii): In a parallelogram, the diagonals bisect each other.**
...