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Assertion (A): The diagonals of a rectangle are equal. Reason (R): A rectangle is a parallelogram with all angles equal to 90°. Which is correct?

Class 9QuadrilateralsGeometry — Quadrilaterals
  • ABoth A and R are true and R is the correct explanation of A
  • BBoth A and R are true but R is not the correct explanation of A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

Both statements are true. Because all angles are 90°, the two triangles formed by a diagonal are congruent (RHS/SAS), making the diagonals equal — so R correctly explains A.
Answer: A) Both A and R are true and R is the correct explanation of A

Key idea: Special parallelograms

**Rectangle** (parallelogram + all angles 90°):
- All properties of a parallelogram.
- Diagonals are EQUAL (in addition to bisecting each other).

**Rhombus** (parallelogram + all sides equal):
- All properties of a parallelogram.
- Diagonals bisect each other AT RIGHT ANGLES.
- Diagonals also bisect the angles of the rhombus.

**Square** (rectangle + rhombus):
- All properties of both.
- Diagonals: equal, bisect at right angles, AND bisect angles.

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