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  • Write down the converse of following statements : (i) If a rectangle ‘R’ is a square, then R is a rhombus.

Write down the converse of the following statements:
(i) If a rectangle ‘R’ is a square, then R is a rhombus.
(ii) If today is Monday, then tomorrow is Tuesday.
(iii) If you go to Agra, then you must visit the Taj Mahal.
(iv) If the sum of the squares of two sides of a triangle is equal to the square of the third side of the triangle, then the triangle is right-angled.
(v) If all three angles of a triangle are equal, then the triangle is equilateral.
(vi) If x: y = 3: 2, then 2x = 3y.
(vii) If S is a cyclic quadrilateral, then the opposite angles of S are supplementary.
(viii) If x is zero, then x is neither positive nor negative.
(ix) If two triangles are similar, then the ratio of their corresponding sides is equal.

Answers (1)

(i) Converse definition: A conditional statement is said to not be logically equivalent to its converse.Thus, Converse: If the rectangle R is a rhombus, then it is square.

(ii) Converse definition: A conditional statement is said to be not logically equivalent to its converse. Thus, Converse: If tomorrow is Tuesday, then today is Monday.

(iii) Converse definition: A conditional statement is said to be not logically equivalent to its converse.Thus, Converse: If you must visit Taj Mahal, then you go to Agra.

(iv) Converse definition: A conditional statement is said to be not logically equivalent to its converse. Thus, Converse: If the triangle is a right triangle, then the sum of the squares of a triangle is equal to the square of the third side.

(v) Converse definition: A conditional statement is said to be not logically equivalent to its converse. Thus, Converse: If the triangle is equilateral, then all three angles of the triangle are equal.

(vi) Converse definition: A conditional statement is said to be not logically equivalent to its converse. Thus, Converse: If 2x = 3y, then x:y = 3:2.

(vii) Converse definition: A conditional statement is said to be not logically equivalent to its converse. Thus, Converse: If the opposite angles of a quadrilateral are supplementary, then S is cyclic.

(viii) Converse definition: A conditional statement is said to be not logically equivalent to its converse. Thus, Converse: If x is neither positive nor negative, then x = 0.

(ix) Converse definition: A conditional statement is said to be not logically equivalent to its converse. Thus, Converse:If the ratio of the corresponding sides of two triangles is equal, then the triangles are similar.

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