MHT CET · Maths · Mathematical Reasoning

If statement I: If a quadrilateral \(A B C D\) is a square, then all of its sides are equal.
Statement II: All the sides of a quadrilateral \(A B C D\) are equal, then \(A B C D\) is a square.
Then

A statement II is an inverse of statement I.
B statement II is a negation of statement I.
C statement II is a converse of statement I.
D statement II is a contrapositive of statement I.

Verified Solution

Answer & Solution

Correct Answer

(C) statement II is a converse of statement I.

Step-by-step Solution

Detailed explanation

Converse of \(p \rightarrow q\) is \(q \rightarrow p\)
Hence, statement-II is converse of statement-I

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If statement I: If a quadrilateral \(A B C D\) is a square, then all of its sides are equal.Statement II: All the sides of a quadrilateral \(A B C D\) are equal, then \(A B C D\) is a square.Then

Step-by-step Solution

If statement I: If a quadrilateral \(A B C D\) is a square, then all of its sides are equal.
Statement II: All the sides of a quadrilateral \(A B C D\) are equal, then \(A B C D\) is a square.
Then