CBSE Class 8 Maths Chapter 9: The Baudhayana-Pythagoras Theorem — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 9: The Baudhāyana-Pythagoras Theorem 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): A square constructed on the diagonal of a square has twice the original square's area.
Reason (R): The diagonal divides the original square into two congruent right triangles, while the new square can be decomposed into four of them.
Reason (R): The diagonal divides the original square into two congruent right triangles, while the new square can be decomposed into four of them.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The area ratio is 4:2 = 2.
2
Assertion (A): Doubling the side of a square makes its area four times as large.
Reason (R): The hypotenuse of a right triangle lies opposite the right angle.
Reason (R): The hypotenuse of a right triangle lies opposite the right angle.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the hypotenuse definition does not explain the scaling of square area.
3
Assertion (A): A square with half the side of another has one-fourth its area.
Reason (R): Halving a square's side always halves its area.
Reason (R): Halving a square's side always halves its area.
Answer: (c)
A is true, but R is false. Area scales as the square of the side-length factor.
4
Assertion (A): The diagonal of a unit square has rational length 2.
Reason (R): Its square is 2, so its length is square root of 2.
Reason (R): Its square is 2, so its length is square root of 2.
Answer: (d)
A is false, but R is true. The diagonal is irrational and approximately 1.414.
5
Assertion (A): In an isosceles right triangle with legs a, the hypotenuse is a square root of 2.
Reason (R): The theorem gives c squared = a squared + a squared = 2a squared.
Reason (R): The theorem gives c squared = a squared + a squared = 2a squared.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Taking the positive square root gives c = a square root of 2.
6
Assertion (A): The hypotenuse is opposite the right angle.
Reason (R): The two legs of an isosceles right triangle are equal.
Reason (R): The two legs of an isosceles right triangle are equal.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but equality of the legs does not define the hypotenuse.
7
Assertion (A): An isosceles right triangle with hypotenuse 10 has each leg 5 square root of 2.
Reason (R): Each leg is 10/2 = 5.
Reason (R): Each leg is 10/2 = 5.
Answer: (c)
A is true, but R is false. Since a square root of 2 = 10, a = 5 square root of 2, not 5.
8
Assertion (A): In every right triangle, the hypotenuse is the shortest side.
Reason (R): The square of the hypotenuse equals the sum of the squares of the legs.
Reason (R): The square of the hypotenuse equals the sum of the squares of the legs.
Answer: (d)
A is false, but R is true. The positive hypotenuse is longer than either leg.
9
Assertion (A): For a right triangle with legs 3 and 4, the hypotenuse is 5.
Reason (R): The relation 3 squared + 4 squared = 5 squared holds.
Reason (R): The relation 3 squared + 4 squared = 5 squared holds.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Nine plus sixteen equals twenty-five.
10
Assertion (A): Squares of areas 9 and 16 can be combined geometrically into a square of area 25.
Reason (R): A right triangle with legs 3 and 4 has area 6.
Reason (R): A right triangle with legs 3 and 4 has area 6.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the triangle's area does not explain the sum of square areas.
11
Assertion (A): If a squared + b squared = c squared for positive side lengths, a triangle with those sides is right-angled.
Reason (R): The converse fails for the side lengths 5, 12 and 13.
Reason (R): The converse fails for the side lengths 5, 12 and 13.
Answer: (c)
A is true, but R is false. The converse is true, and 25 + 144 = 169 confirms that example.
12
Assertion (A): The side lengths 2, 3 and 4 form a right triangle.
Reason (R): For these lengths, 2 squared + 3 squared is not equal to 4 squared.
Reason (R): For these lengths, 2 squared + 3 squared is not equal to 4 squared.
Answer: (d)
A is false, but R is true. Thirteen is not sixteen.
13
Assertion (A): The theorem compares areas of squares built on the three sides of a right triangle.
Reason (R): Area on the hypotenuse equals the sum of the areas on the two legs.
Reason (R): Area on the hypotenuse equals the sum of the areas on the two legs.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. This is the geometric content of the theorem.
14
Assertion (A): A square of area 50 has side 5 square root of 2.
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 equality of the four sides does not verify the numerical square root.
15
Assertion (A): The square root of 2 lies between 1.4 and 1.5.
Reason (R): Both 1.4 squared and 1.5 squared are less than 2.
Reason (R): Both 1.4 squared and 1.5 squared are less than 2.
Answer: (c)
A is true, but R is false. 1.4 squared is 1.96, but 1.5 squared is 2.25.
16
Assertion (A): The square root of 2 equals exactly 1.414.
Reason (R): Squaring 1.414 gives 1.999396, not exactly 2.
Reason (R): Squaring 1.414 gives 1.999396, not exactly 2.
Answer: (d)
A is false, but R is true. The decimal is an approximation.
17
Assertion (A): A dissection proof rearranges pieces without changing their total area.
Reason (R): Congruent pieces retain their areas when moved or rotated.
Reason (R): Congruent pieces retain their areas when moved or rotated.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Area preservation makes the rearrangement a valid proof.
18
Assertion (A): The theorem can be used to find a missing side of a right triangle.
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 the property of a square does not explain every missing-side computation.
19
Assertion (A): For legs 6 and 8, the hypotenuse is 10.
Reason (R): The value is found from c = 6 + 8.
Reason (R): The value is found from c = 6 + 8.
Answer: (c)
A is true, but R is false. The correct calculation is c = square root of (36 + 64) = 10.
20
Assertion (A): The theorem applies unchanged to any triangle regardless of its angles.
Reason (R): Its standard side relation is specific to right triangles.
Reason (R): Its standard side relation is specific to right triangles.
Answer: (d)
A is false, but R is true. Non-right triangles do not generally satisfy a squared + b squared = c squared.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 9 The Baudhayana-Pythagoras Theorem?
This chapter covers all key topics from The Baudhayana-Pythagoras Theorem 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?
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