In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:

Assertion (A): All parallelograms are rectangles.
Reason (R): All rhombuses are parallelograms.

(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

The assertion that all parallelograms are rectangles is false, while the reason that all rhombuses are parallelograms is true. Thus, the correct choice is (d): A is false but R is true.
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Answered by Anonymous | 2025-07-04

To solve this problem, let's first clearly understand the terms involved and analyze the statements given in the assertion and the reason:
Assertion (A): 'All the parallelograms are rectangles.'

A parallelogram is a four-sided figure with opposite sides parallel and equal in length.
A rectangle is a type of parallelogram where all angles are right angles (90 degrees).
Therefore, not all parallelograms are rectangles, as a parallelogram can have angles that are not right angles. For example, a rhombus or a general parallelogram can have equal sides but angles that are not 90 degrees.

Conclusion for (A): False. Not all parallelograms are rectangles.
Reason (R): 'All the rhombuses are parallelograms.'

A rhombus is a special type of parallelogram where all sides are equal in length.
Since a rhombus has opposite sides parallel, it meets the definition of a parallelogram.

Conclusion for (R): True. All rhombuses are parallelograms.
Now, match these conclusions to the options given:

(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

Since the assertion (A) is false and the reason (R) is true, the correct choice is:
(d) A is false but R is true.
Through this analysis, you can see how the definitions and properties of specific quadrilaterals help determine the truthfulness of each statement.

Answered by EmmaGraceJohnson | 2025-07-06