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

(i) The letter N has one line of symmetry.

(ii) Every hexagon has six lines of symmetry.

(iii) All right angled triangles have one line of symmetry.

(iv) A triangle with more than one line of symmetry must be an equilateral triangle.

(v) A line of symmetry divides a figure into two identical parts.

(vi) A circle has only 8 lines of symmetry.

(vii) A regular octagon has 10 lines of symmetry.

(viii) A square and a rectangle have the same number of lines of symmetry.

(ix) A right angled triangle can have atmost one line of symmetry.

(x) If an isosceles triangle has more than one line of symmetry, then it must be an equilateral triangle.

(xi) If a rectangle has more than two lines of symmetry, then it must be a square.

(i) False
Reason — The letter N has no line of symmetry. It only has rotational symmetry of order 2.

(ii) False
Reason — Only a regular hexagon has six lines of symmetry. An irregular hexagon may have fewer or no lines of symmetry.

(iii) False
Reason — Only an isosceles right-angled triangle has one line of symmetry. A scalene right-angled triangle has no line of symmetry.

(iv) True
Reason — Only an equilateral triangle has more than one (in fact, three) lines of symmetry.

(v) True
Reason — A line of symmetry divides a figure into two coincident (mirror-image) parts, which are identical in shape and size.

(vi) False
Reason — A circle has an infinite number of lines of symmetry (every diameter is a line of symmetry).

(vii) False
Reason — A regular octagon has 8 lines of symmetry, not 10.

(viii) False
Reason — A square has 4 lines of symmetry, while a rectangle has only 2 lines of symmetry.

(ix) True
Reason — A right-angled triangle has at most one line of symmetry (in the case of an isosceles right-angled triangle). A scalene right-angled triangle has none.

(x) True
Reason — An isosceles triangle has exactly one line of symmetry. If it has more than one, the third side must also be equal, making it an equilateral triangle.

(xi) True
Reason — A rectangle has exactly two lines of symmetry. If it has more (such as the diagonals), all its sides must be equal, making it a square.