Question

1) Write down the converse of the following statement:

(i) If rectangle ${}^{\prime }{R}^{\prime }$ is a square, then R is a rhombus.

2) Write down the converse of the following statement:

(ii) If tody is Monday then tomorrow is Tuesday.

3) Write down the converse of the following statement:

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

4) Write down the converse of the following statement:

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.

5) Write down the converse of the following statement:

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

6) Write down the converse of the following statement:

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

7) Write down the converse of the following statement:

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

8) Write down the converse of the following statement:

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

9) Write down the converse of the following statement:

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

Answer 1

Solution:

1) Given statement: ''If a rectangle R is a square, then R is a rhombus''

Let p : Rectangle R is a square.

q : Rectangle R is a rhombus.

Now, Converse of given statement $p\to q$ is $q\to p$

If a rectangle R is a rhombus, then it is a square.

2) Given statement : ''If today is Monday, then tomorrow is Tuesday''

Let p : Today is Monday.

q : Tomorrow is Tuesday.

Now, Converse of given statement $p\to q$ is $q\to p$

If tomorrow is Tuesday, then today is Monday.

3) Given statement : ''If you go to Agra, then you must visit Taj Mahal''

Let p : You go to Agra.

q : You must visit Taj Mahal.

Now, Converse of given statement $p\to q$ is $p\to q$

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

4) Given statement : ''If the sum of squres of two sides of a triangle is equal to the square of third side of a triangle, then the triangle is right angled.''

Let p : The sum of squares of two sides of a triangle is equal to the square of third side of a triangle.

q : The triangle is right angled triangle.

Now, Converse of given statement $p\to q$ is $q\to p$

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

5) Given statement : ''If all three angles of a triangle are equal, then the triangle is equilateral''

Let p : All three angles of a triangle are equal.
q : The triangle is equilateral.

Now, Converse of given statement $p\to q$ is $q\to p$

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

6) Given statement : ''If $x:y=3:2,$'' then $2x=3y{.}^{\prime \prime }$

Let p : $x:y=3:2,$

q : $2x=3y$

Now, Coverse of given statement $p\to q$ is $q\to p$

If $2x=3y$ then $x:y=3:2$

7) Given statement: ''If S is a cyclic quadrilateral, then the opposite angles of S are supplementary''

Let p : S is a cyclic quadrilateral.

q : The opposite angles of S are supplementary.

Now, Converse of given statement $p\to q$ is $q\to p$

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

8) Given statement : ''If x is zero, then x is neither positive nor negative.''

Let p : x is zero.

q : x is neither positive nor negative.

Now, Converse of given statement $p\to q$ is $q\to p$

If x is neither positive nor negative, then x is zero.

9) Given statement: ''If two triangles are similar, then the ratio of their corresponding sides are equal''

Let p : Two triangles are similar.

q : The ratio of their corresponding sides are equal.

Now, Converse of given statement $p\to q$ is $p\to q$

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