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

(i) Each angle of an equilateral triangle is a right angle.

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

(iii) The diagonals of a rectangle are equal in length.

(iv) The diagonals of a rectangle are perpendicular to one another.

(v) The diagonals of a rhombus are equal in length.

(vi) Any three line segments make up a triangle.

(vii) All the faces of a triangular prism are triangles.

(viii) All the faces of a triangular pyramid are triangles.

(i) False
Reason — Each angle of an equilateral triangle is 60°, not 90° (right angle).

(ii) False
Reason — In a rectangle, only opposite sides are equal in length, not adjacent sides. If adjacent sides are equal, it becomes a square.

(iii) True
Reason — The diagonals of a rectangle are equal in length.

(iv) False
Reason — The diagonals of a rectangle bisect each other but are not perpendicular. They are perpendicular only in a square.

(v) False
Reason — The diagonals of a rhombus bisect each other at right angles but are generally not equal in length. They are equal only in a square.

(vi) False
Reason — Three line segments can form a triangle only if the sum of the lengths of any two sides is greater than the third side (triangle inequality).

(vii) False
Reason — A triangular prism has 2 triangular faces and 3 rectangular faces, so not all faces are triangles.

(viii) True
Reason — A triangular pyramid (tetrahedron) has 4 triangular faces — 1 triangular base and 3 triangular side faces.