Question

Read the following statements and choose the correct option.
Assertion (A): If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Reason (R): In a parallelogram, diagonals bisect each other.

• A. Both A and R are true, and R is the correct explanation of A.
• B. Both A and R are true, but R is not the correct explanation of A.
• C. A is true, but R is false.
• D. A is false, but R is true.

Hint:

For Assertion-Reason questions, evaluate A and R independently first. Only after confirming both are true, ask: ``Does R logically explain or justify why A is true?'' Here, R states the property of parallelograms (diagonals bisect each other), and A uses this as a characterization — so R is indeed the correct explanation of A.

Answer 1

The Correct Option is A

Step 1: Understand the question type.
This is an assertion and reason question. We check if the assertion is true, if the reason is true, and then whether the reason properly explains the assertion.

Step 2: Test the assertion.
The assertion says if the diagonals of a quadrilateral bisect each other, then it is a parallelogram. This is a known theorem in geometry, so the assertion is true.

Step 3: Why the assertion holds.
If diagonals bisect each other, the two triangles formed are congruent, which makes opposite sides equal and parallel. That is exactly the definition of a parallelogram.

Step 4: Test the reason.
The reason says in a parallelogram the diagonals bisect each other. This is also a true and standard property of parallelograms.

Step 5: Check the explanation link.
The reason is exactly the fact used to prove the assertion, so it does explain why the assertion is true.

Step 6: Choose the option.
Both statements are true and the reason explains the assertion. So the answer is \[ \boxed{\text{Both A and R are true, and R is the correct explanation of A}} \]