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Assertion: In...

Question

Assertion: In a quadrilateral ABCD, we have (AB + BC + CD + DA) > 2AC.

Reason: The sum of any two sides of a triangle is greater than the third side.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

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Solution

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
We know that sum of any two sides of a triangle is greater than the third side.
Therefore, $(A B + B C) > A C$ and $(C D + D A) > A C$ .
Adding them, we get:
$(A B + B C + C D + D A) > 2 A C$
Thus, the assertion is true, and the reason gives the assertion.

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Standard IX Mathematics