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Write down the converse of following statements: If two triangles are similar, then the ratio of their corresponding sides are equal.

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प्रश्न

Write down the converse of following statements:

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

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उत्तर

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

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अध्याय 14: Mathematical Reasoning - Exercise [पृष्ठ २६४]

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एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
अध्याय 14 Mathematical Reasoning
Exercise | Q 10.(ix) | पृष्ठ २६४

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संबंधित प्रश्न

Write the contrapositive and converse of the following statements.

If x is a prime number, then x is odd


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Something is cold implies that it has low temperature.


Write the contrapositive and converse of the following statements.

x is an even number implies that x is divisible by 4


Write each of the following statement in the form “if-then”.

You get a job implies that your credentials are good.


Write each of the following statement in the form “if-then”.

A quadrilateral is a parallelogram if its diagonals bisect each other.


Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other.

(a) If you live in Delhi, then you have winter clothes.

(i) If you do not have winter clothes, then you do not live in Delhi.

(ii) If you have winter clothes, then you live in Delhi.

(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other.

(i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.

(ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.


State the converse and contrapositive of each of the following statements:

p: A positive integer is prime only if it has no divisors other than 1 and itself.

 


State the converse and contrapositive of each of the following statements:

q: I go to a beach whenever it is a sunny day.


Re write each of the following statements in the form “p if and only if q”.

q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.


State the converse and contrapositive of  statement:

I go to a beach whenever it is a sunny day.


State the converse and contrapositive of  statement:

If you live in Delhi, then you have winter clothes.


Rewrite of the  statement in the form "p if and only if q".

 p : If you watch television, then your mind is free and if your mind is free, then you watch television.


Determine the contrapositive of the statement:

 If Mohan is a poet, then he is poor.


Determine the contrapositive of the statement:

 Only if Max studies will he pass the test.


Determine the contrapositive of the statement:

 It never rains when it is cold.


Determine the contrapositive of the statement:

If x is less than zero, then x is not positive.


Determine the contrapositive of the statement:

 If he has courage he will win.


Determine the contrapositive of the statement:

Only if he does not tire will he win.


Show that the following statement is true.
p: For any real numbers x, y if x = y, then 2x + a = 2y + a when a ∈ Z.


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If x = y and y = 3, then x = 3.


Write down the contrapositive of the following statements:

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


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If x and y are negative integers, then xy is positive.


Write down the contrapositive of the following statements:

If x is a real number such that 0 < x < 1, then x2 < 1.


Write down the converse of following statements:

If a rectangle ‘R’ is a square, then R is a rhombus.


Write down the converse of following statements:

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


Write down the converse of following statements:

If x : y = 3 : 2, then 2x = 3y.


Using contrapositive method prove that if n2 is an even integer, then n is also an even integers.


The converse of the statement “If sun is not shining, then sky is filled with clouds” is ______.


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Write the statement in the form “if p, then q”.

p: It is necessary to have a password to log on to the server.


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