CBSE Class 8 Maths Chapter 4: Quadrilaterals — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 4: Quadrilaterals from the NCERT Class 8 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(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.
(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.
Assertion & Reason Questions
1
Assertion (A): The interior angles of any quadrilateral sum to 360 degrees.
Reason (R): A diagonal can divide it into two triangles whose angle sums are 180 degrees each.
Reason (R): A diagonal can divide it into two triangles whose angle sums are 180 degrees each.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Adding the two triangle sums gives 360 degrees.
2
Assertion (A): A rectangle has four right angles.
Reason (R): A square has four equal sides.
Reason (R): A square has four equal sides.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but equal sides of a square do not explain a rectangle's angles.
3
Assertion (A): Every square is a rectangle.
Reason (R): A square fails the requirement of having four right angles.
Reason (R): A square fails the requirement of having four right angles.
Answer: (c)
A is true, but R is false. A square has four right angles and therefore satisfies the rectangle definition.
4
Assertion (A): Every rectangle is a square.
Reason (R): A rectangle need not have all four sides equal.
Reason (R): A rectangle need not have all four sides equal.
Answer: (d)
A is false, but R is true. Only rectangles with all sides equal are squares.
5
Assertion (A): Opposite sides of a parallelogram are parallel and equal.
Reason (R): A diagonal divides a parallelogram into two congruent triangles.
Reason (R): A diagonal divides a parallelogram into two congruent triangles.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Congruence yields equality of opposite sides, alongside parallel structure.
6
Assertion (A): Opposite angles of a parallelogram are equal.
Reason (R): The diagonals of a rectangle are equal.
Reason (R): The diagonals of a rectangle are equal.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the rectangle's diagonals do not explain parallelogram angles.
7
Assertion (A): The diagonals of a general parallelogram bisect each other.
Reason (R): They are always equal in length.
Reason (R): They are always equal in length.
Answer: (c)
A is true, but R is false. Equality is not a general parallelogram property.
8
Assertion (A): The diagonals of a rectangle are perpendicular in every case.
Reason (R): They are equal and bisect each other.
Reason (R): They are equal and bisect each other.
Answer: (d)
A is false, but R is true. They need not meet at right angles.
9
Assertion (A): A rhombus has four equal sides.
Reason (R): It is a parallelogram with all sides equal.
Reason (R): It is a parallelogram with all sides equal.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. This classification gives its side property.
10
Assertion (A): The diagonals of a rhombus bisect each other at right angles.
Reason (R): The diagonals of a rectangle are equal.
Reason (R): The diagonals of a rectangle are equal.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the rectangle property does not explain the rhombus property.
11
Assertion (A): A rhombus need not have four right angles.
Reason (R): Every rhombus is automatically a rectangle.
Reason (R): Every rhombus is automatically a rectangle.
Answer: (c)
A is true, but R is false. Only a rhombus with right angles is a square.
12
Assertion (A): A square's diagonals are unequal.
Reason (R): They are equal, perpendicular, and bisect each other.
Reason (R): They are equal, perpendicular, and bisect each other.
Answer: (d)
A is false, but R is true. A square combines rectangle and rhombus diagonal properties.
13
Assertion (A): A kite has two pairs of equal adjacent sides.
Reason (R): The equal pairs are non-overlapping adjacent pairs.
Reason (R): The equal pairs are non-overlapping adjacent pairs.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. That side arrangement defines a kite in the chapter.
14
Assertion (A): A trapezium has at least one pair of parallel opposite sides.
Reason (R): A parallelogram has two pairs of parallel opposite sides.
Reason (R): A parallelogram has two pairs of parallel opposite sides.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the parallelogram definition does not explain every trapezium.
15
Assertion (A): A kite need not be a parallelogram.
Reason (R): Every kite has both pairs of opposite sides parallel.
Reason (R): Every kite has both pairs of opposite sides parallel.
Answer: (c)
A is true, but R is false. Its defining equalities concern adjacent sides.
16
Assertion (A): A quadrilateral with one pair of parallel sides must be a rectangle.
Reason (R): A trapezium can have only one pair of parallel sides and no right angles.
Reason (R): A trapezium can have only one pair of parallel sides and no right angles.
Answer: (d)
A is false, but R is true. The condition is insufficient for a rectangle.
17
Assertion (A): A quadrilateral can often be classified in more than one category.
Reason (R): A square is simultaneously a rectangle, rhombus and parallelogram.
Reason (R): A square is simultaneously a rectangle, rhombus and parallelogram.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The example shows nested definitions.
18
Assertion (A): If three angles of a quadrilateral are 90 degrees, the fourth is 90 degrees.
Reason (R): The angle sum of a triangle is 180 degrees.
Reason (R): The angle sum of a triangle is 180 degrees.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the triangle fact does not directly state the quadrilateral computation.
19
Assertion (A): A parallelogram with one right angle is a rectangle.
Reason (R): Its other three angles may remain non-right angles.
Reason (R): Its other three angles may remain non-right angles.
Answer: (c)
A is true, but R is false. Adjacent and opposite angle relations force all four to be right angles.
20
Assertion (A): A rhombus with equal diagonals cannot be a square.
Reason (R): A rhombus whose diagonals are also equal has the rectangle property and is a square.
Reason (R): A rhombus whose diagonals are also equal has the rectangle property and is a square.
Answer: (d)
A is false, but R is true. The extra property identifies a square.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 4 Quadrilaterals?
This chapter covers all key topics from Quadrilaterals as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 8 board exam preparation covering the complete syllabus.
Are these CBSE Class 8 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 8 Maths?
All chapters of CBSE Class 8 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study Quadrilaterals online for free?
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