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Assertion (A): A square is a rectangle. Reason (R): A rectangle is a parallelogram with all angles equal to 90°, and a square has all angles 90°. Which is correct?

Class 8Understanding QuadrilateralsQuadrilaterals
  • ABoth A and R are true, and R correctly explains A
  • BBoth A and R are true, but R does not explain A
  • CA is true, R is false
  • DA is false, R is true

Step-by-Step Solution

A square has four 90° angles and is a parallelogram, so it meets the rectangle definition. R states that definition and is the reason A holds. Both true and R explains A.
Answer: A) Both A and R are true, and R correctly explains A

Key idea: Special parallelograms — extra properties

**Rectangle**: parallelogram + all angles 90°. Extra: diagonals are equal in length.

**Rhombus**: parallelogram + all sides equal. Extra: diagonals are perpendicular AND bisect the angles at each vertex.

**Square**: parallelogram + all angles 90° + all sides equal. Has both extras: equal AND perpendicular AND angle-bisecting diagonals.

Knowing the family tree saves you memorising overlapping rules — a square inherits everything from rectangle AND rhombus.

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