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Mathematics

Assertion (A) : If one angle of a parallelogram measures 90°, the parallelogram is rectangle.

Reason (R) : If each interior angle of parallelogram is 90°, then all sides of it are equal.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Quadrilaterals

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Answer

If one angle is 90°, the opposite angle is also 90° as opposite angles of a parallelogram are equal.

If one angle is 90°, the adjacent angle is 180° - 90° = 90°, as the sum of adjacent angles in a rectangle is 180°.

Thus, all angles of parallelogram are 90° if one angle is 90°.

Therefore, the parallelogram is a rectangle.

So, assertion (A) is true.

A parallelogram with all interior angles equal to 90° is a rectangle, but not necessarily a square. Therefore, all sides are not necessarily equal.

So, reason (R) is false.

∴ A is true, but R is false.

Hence, option 3 is the correct option.

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