State whether the following statements are true (T) or false (F):

(i) Each angle of a rectangle is a right angle.

(ii) The opposite sides of a rectangle are equal in length.

(iii) The diagonals of a square are perpendicular to one another.

(iv) All sides of a rhombus are equal in length.

(v) All sides of a parallelogram are equal in length.

(vi) The opposite sides of a trapezium are parallel.

(vii) The diagonals of a parallelogram are equal.

(i) True
Reason — By definition, all four interior angles of a rectangle are right angles (90°).

(ii) True
Reason — Since every rectangle is a parallelogram, its opposite sides are equal in length.

(iii) True
Reason — The diagonals of a square intersect at right angles (since a square is also a rhombus).

(iv) True
Reason — By definition, all four sides of a rhombus are equal in length.

(v) False
Reason — In a parallelogram, only opposite sides are equal in length, not all sides. If all sides are equal, it becomes a rhombus.

(vi) False
Reason — In a trapezium, only one pair of opposite sides is parallel, not both pairs.

(vii) False
Reason — The diagonals of a parallelogram bisect each other but are not necessarily equal. They are equal only in a rectangle or a square.