If the diagonals of a quadrilateral bisect each other, it is a __________.

Theorem 8.7 : If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Given the following statements : If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. Identify these as contrapositive or converse of each other.

Given below are some pairs of statements. Combine each pair using if and only if: (i) p: If a quadrilateral-is equiangular, then it is a rectangle. q: If a quadrilateral is a rectangle, then it is equiangular. (ii) p: If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. q: If a number is divisble by 3, then the sum of its digits is divisible by 3. (iii) p: A quadrilateral is a parallelogram if its diagonals bisect each other. q: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. (iv) p: If f(a) = 0, then (x -a) is a factor of polynomial f(x). q: If (x-a) is a factor of polynomial f(x), thenf(a) = 0. (v) p: If a square matrix A is invertible, then |A| is nonzero. q: If A is a square matrix such that |A| is nonzero, then A is invertible.

Write the converse and contrapositive of each of the following: (i) If xis a prime number, then xis odd. (ii) If a positive integer n is divisible by 9, then the sum of its digits is divisible by 9. (iii) If the two lines are parallel, then they do not intersect in the same plane. (iv) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. (v) If A and Bare subsets of X such that A sube B, then (X-B) sube (X-A). (vi) If f(2) = 0, then f(x) is divisible by (x-2). (vii) If you were born in India, then you are a citizen of India. (viii) If it rains, then I stay at home.

The diagonals of a parallelogram bisect each other.

The diagonals of a parallelogram bisect each other.

If the diagonals of a quadrilateral bisect each other at right angles, then this quadrilateral is