**Question:**

**Write down the converse of following statements :**

**(i) If a rectangle â€˜Râ€™ 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 Taj Mahal.**

**(iv) If the sum of squares of two sides of a triangle is equal to the square of third side of a 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 are equal.**

**Solution:**

**(i) If a rectangle â€˜Râ€™ is a square, then R is a rhombus.**

We know that a conditional statement is not logically equivalent to its converse.

Converse: If the rectangle R is rhombus, then it is square.

**(ii) If today is Monday, then tomorrow is Tuesday.**

We know that a conditional statement is not logically equivalent to its converse.

Converse: If tomorrow is Tuesday, then today is Monday.

(iii) If you go to Agra, then you must visit Taj Mahal.

**Solution:**

We know that a conditional statement is not logically equivalent to its converse.

Converse: If you must visit Taj Mahal, then you go to Agra.

**(iv) If the sum of squares of two sides of a triangle is equal to the square of third side of a triangle, then the triangle is right angled.**

We know that a conditional statement is not logically equivalent to its converse.

Converse: If the triangle is right triangle, then the sum of the squares of two sides of a triangle is equal to the square of third side.

**(v) If all three angles of a triangle are equal, then the triangle is equilateral.**

We know that a conditional statement is not logically equivalent to its converse.

Converse: If the triangle is equilateral, then all three angles of the triangle are equal.

**(vi) If x: y = 3 : 2, then 2x = 3y.**

We know that a conditional statement is not logically equivalent to its converse.

Converse: if 2x = 3y then x: y = 3: 2

(vii) If S is a cyclic quadrilateral, then the opposite angles of S are supplementary.

We know that a conditional statement is not logically equivalent to its converse.

Converse: If the opposite angles of a quadrilateral are supplementary, then S is cyclic.

**(viii) If x is zero, then x is neither positive nor negative.**

We know that a conditional statement is not logically equivalent to its converse.

Converse: If x is neither positive nor negative then x = 0

**(ix) If two triangles are similar, then the ratio of their corresponding sides are equal.**

We know that a conditional statement is not logically equivalent to its converse.

Converse: If the ratio of corresponding sides of two triangles are equal, then triangles are similar.

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