Write the converses of the following statements. Also, decide in each case whether the converse is true or false.

(i) If triangle ABC is isosceles, then its base angles are equal.

(ii) If an integer is odd, then its square is an odd integer.

(iii) If x² = 1, then x = 1.

(iv) If ABCD is a parallelogram, then AC and BD bisect each other.

(v) If a, b and c, are whole numbers, then a + (b + c) = (a + b) + c.

(vi) If x and y are two odd numbers, then x + y is an even number.

(vii) If vertices of a parallelogram lie on a circle, then it is a rectangle.

Suppose a + b = c + d, and a < c. Use proof by contradiction to show b > d.

Use proof by contradiction to prove that if for an integer a, a² is even, then so is a.

Use proof by contradiction to prove that if for an integer a, a² is divisible by 3, then a is divisible by 3.