Write the converses of the following statements. Also, decide in each case whether the converse is true or false.
If triangle ABC is isosceles, then its base angles are equal.
Converse: If the base angles of triangle ABC are equal, then it is an isosceles triangle. True.
If an integer is odd, then its square is an odd integer.
Converse: If the square of an integer is odd, then the integer is odd. True.
If , then .
Converse: If x = 1, then x² = 1. True.
If ABCD is a parallelogram, then AC and BD bisect each other.
Converse: If diagonals AC and BD of quadrilateral ABCD bisect each other, then ABCD is a parallelogram. True.
If and , are whole numbers, then .
Converse: If a + (b + c) = (a + b) + c, then a, b and c are whole numbers. False.
If and are two odd numbers, then is an even number.
Converse: If x + y is an even number, then x and y are odd numbers. False.
If vertices of a parallelogram lie on a circle, then it is a rectangle.
Converse: If a parallelogram is a rectangle, then its vertices lie on a circle. True.
Explanation
The converse of a statement 'If p, then q' is 'If q, then p'. For (v), the associative property holds for all real numbers, not just whole numbers, so the converse is false. For (vi), a counter-example is x = 2, y = 4 (both even), yet x + y = 6 is even.