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Mathematics

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.

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Answer

(i) If the base angles of triangle ABC are equal, then it is isosceles. This is a true statement.

(ii) If the square of an integer is odd, then the integer is odd. This is a true statement.

(iii) If x = 1, then x2 = 1. This is a true statement.

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

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

(vi) If x + y is an even number, then x and y are odd. This is a false statement.

(vii) If a parallelogram is a rectangle, its vertices lie on a circle. This is a true statement.

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