Quadrilaterals — Assertion-Reason Type Questions

Assertion (A) : The two diagonals of a rectangle are equal and bisect each other at right angles.

Reason (R) : Every rectangle is a square.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Answer

The diagonals of a rectangle are equal in length and bisect eah other, but not necessarily at right angles.

∴ Assertion (A) is false.

A square is a special type of rectangle where all sides are equal, but a rectangle is not necessarily a square.

A rectangle only requires four right angles; it does not require all four sides to be equal.

Every square is a rectangle, but not every rectangle is a square.

∴ Reason (R) is false.

Both A and R are false.

Hence, option 4 is the correct option.

Assertion (A) : If diagonals of a quadrilateral are equal, then it must be a rectangle.

Reason (R) : The diagonals of a rectangle are equal.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Answer

For a quadrilateral to be a rectangle, the diagonals must be equal and they must bisect each other.Having equal diagonals is not enough to say a quadrilateral to be a rectangle.

Assertion (A) is false.

This is a fundamental property of rectangles.

If we have a rectangle ABCD, we can prove the diagonals AC and BD are equal using the SAS congruence rule on △ABC and △DCB.

AB = DC (Opposite sides)

∠B = ∠C = 90°

BC = BC (Common side)

Therefore, AC = BD.

Reason (R) is true.

A is false, R is true

Hence, option 2 is the correct option.

Assertion (A) : Every square is a parallelogram.

Reason (R) : In a square as well as in a parallelogram, the diagonals are equal in length.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Answer

By definition, a parallelogram is a quadrilateral with two pairs of parallel opposite sides.

A square has all the properties of a parallelogram:

Opposite sides are parallel.

Opposite sides are equal.

Opposite angles are equal.

Diagonals bisect each other.

Because a square meets all these criteria, it is considered a special type of parallelogram.

Assertion (A) is true.

A square has equal diagonals, it is not true for a general parallelogram.

In a standard parallelogram (like a rhombus or a slanted parallelogram), one diagonal is typically longer than the other.

Reason (R) is false.

A is true, R is false.

Hence, option 1 is the correct option.