 # Write down the converse of following statements : `
Question:

Write down the converse of 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 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 ‘R’ 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.