For statement : "If a quadrilateral ABCD is rhombus then its opposite sides are parallel", its contrapositive and converse are respectively given by
(A)i) If opposite sides of a quadrilateral ABCD are parallel, then quadrilateral ABCD is a rhombus ii) If opposite sides of a quadrilateral ABCD are not parallel, then the quadrilateral ABCD is a rhombus
(B)i) If opposite sides of a quadrilateral ABCD are parallel, then quadrilateral ABCD is not a rhombus ii) If opposite sides of a quadrilateral ABCD are parallel, then quadrilateral ABCD is a rhombus
(C)i) If opposite sides of a quadrilateral ABCD are not parallel, then quadrilateral ABCD is not a rhombus ii) If opposite sides of a quadrilateral ABCD are parallel then quadrilateral ABCD is a rhombusCorrect
(D)i) If opposite sides of a quadrilateral ABCD are parallel, then quadrilateral ABCD is not a rhombus ii) If opposite sides of a quadrilateral ABCD are not parallel, then quadrilateral ABCD is a rhombus
Answer: (C)
Solution
Let p: "ABCD is a rhombus" and q: "opposite sides of ABCD are parallel"; the statement is . Its contrapositive is : "If opposite sides are not parallel, then ABCD is not a rhombus". Its converse is : "If opposite sides are parallel, then ABCD is a rhombus". Only option
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