Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
Assertion (A) : All squares are rectangles.
Reason (R) : A rectangle is a quadrilateral with opposite sides equal and parallel, and a square satisfies these conditions.
In light of the above statements, choose the correct answer from the options given below.
Let:
= The set of all Squares.
= The set of all Rectangles.
= The set of Quadrilaterals with opposite sides equal, parallel, and four right angles.
1. Verification of Assertion (A):
By mathematical definition, a rectangle is a quadrilateral with four right angles (). Since a square also has four right angles and equal opposite sides, it satisfies every requirement to be a rectangle.
Therefore, Assertion (A) is true.
2. Verification of Reason (R):
A rectangle requires:
Opposite sides to be equal and parallel ( and ).
All interior angles to be .
Since a square has all four sides equal (), it mathematically follows that its opposite sides are equal:
Because the square fulfills these criteria, Reason (R) is also true.
The reason provides the specific geometric criteria that a square meets in order to be classified as a rectangle.
