Given the statement: "If a quadrilateral is a parallelogram,then its diagonals bisect each other."
Identify the following statements as the contrapositive or converse of the given statement:
$(i)$ If the diagonals of a quadrilateral do not bisect each other,then the quadrilateral is not a parallelogram.
$(ii)$ If the diagonals of a quadrilateral bisect each other,then it is a parallelogram.
Identify the following statements as the contrapositive or converse of the given statement:
$(i)$ If the diagonals of a quadrilateral do not bisect each other,then the quadrilateral is not a parallelogram.
$(ii)$ If the diagonals of a quadrilateral bisect each other,then it is a parallelogram.
(N/A) Let $P$ be the statement "$A$ quadrilateral is a parallelogram" and $Q$ be the statement "Its diagonals bisect each other". The given statement is $P \implies Q$.
$(i)$ The statement "If the diagonals of a quadrilateral do not bisect each other,then the quadrilateral is not a parallelogram" is of the form $\neg Q \implies \neg P$,which is the contrapositive of $P \implies Q$.
$(ii)$ The statement "If the diagonals of a quadrilateral bisect each other,then it is a parallelogram" is of the form $Q \implies P$,which is the converse of $P \implies Q$.
$(i)$ The statement "If the diagonals of a quadrilateral do not bisect each other,then the quadrilateral is not a parallelogram" is of the form $\neg Q \implies \neg P$,which is the contrapositive of $P \implies Q$.
$(ii)$ The statement "If the diagonals of a quadrilateral bisect each other,then it is a parallelogram" is of the form $Q \implies P$,which is the converse of $P \implies Q$.
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