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Pythagoras Theorem

Assertion AIn...

Question

Assertion (A)
In an isosceles ∆ABC, if ∠C = 90°, then AB² = 3AC².
Reason (R)
In an isosceles ∆ABC, if AC = BC and AB² = 2AC², then ∠C = 90°.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A)
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

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Solution

(d) Assertion (A) is false and Reason (R) is true.

In triangle ABC, let BC be equal to AC.
We have:
$∠ C = 90 °$
Thus,
^{$A B^{2} = A C^{2} + B C^{2} = A C^{2} + A C^{2} (∵ A C = B C) \Rightarrow A B^{2} = 2 A C^{2}$}

Assertion (A) is false.
This proves that Reason (R) is true.

Hence, Assertion (A) is false and Reason (R) is true.

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Reason (R)
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This question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

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