NCERT Solutions for Class 8 Mathematics Ganita Prakash Part II Chapter 2
NCERT solutions for Class 8 Mathematics Chapter The Baudhāyana-Pythagoras Theorem – complete answers & explanations
In this blog, we will explore the NCERT solutions for Class 8 Mathematics, specifically Chapter "The Baudhāyana-Pythagoras Theorem." This chapter introduces important concepts in geometry related to right-angled triangles. Students will learn about various properties of squares, hypotenuses, and the relationships between the sides of triangles. The chapter also delves into fascinating historical context, such as the Baudhāyana theorem and its application in real-world geometry problems. Download the worksheet and practice alongside solutions for better clarity. Book a free trial now to get expert guidance.
What this NCERT chapter covers?
1. The Baudhāyana-Pythagoras Theorem, which relates
the sides of a right-angled triangle.
2. Doubling and halving the area of a square through geometric constructions.
3. Properties and relationships of squares, including the diagonal and hypotenuse.
4. Applications of the theorem in solving geometric problems such as finding missing side lengths and solving real-life problems.
5. Historical insights into Baudhāyana’s contributions to geometry.
6. Working with Pythagorean triples and understanding their significance.
7. Exploring the decimal representation of square roots and their irrationality.
How to use these NCERT solutions?
1. First, attempt the questions in
your worksheet on your own to reinforce the concepts.
2. Compare your answers with the solutions provided here to check your understanding.
3. Parents or teachers can guide students by explaining the concepts in a detailed manner.
4. The solutions follow the worksheet order exactly, making it easier to follow step-by-step.
Important tips & tricks for students
1. Be careful with the basic properties of squares and right-angled triangles, especially the Pythagorean theorem.
2. Focus on understanding the relationships between the sides of a triangle (e.g., a² + b² = c²).
3. For open-ended or student-generated answers, remember that answers may vary.
4. Make sure to visualize constructions for geometric problems, as this helps to better understand the problem and solution.
5. Practice problems involving Pythagorean triples and their applications to strengthen your geometry skills.
NCERT solutions – complete answer key
2.1 Doubling a square
- How can one construct a square having double the area of a given square?
The diagonal of a square produces a square of double the area of the original square.
- Why does the new dotted square have double the area of the original square?
The new square is made up of four small congruent triangles, and the original square is made up of two small triangles.
2.2 Halving a square
- How would you construct a square whose area is half that of the original square?
We can reverse the construction of doubling a square by drawing a tilted smaller square inside the larger one.
- Why is the smaller inside square half the area of the larger square?
Adding horizontal and vertical lines helps demonstrate that the smaller square has half the area of the larger square.
2.3 Hypotenuse of an isosceles right triangle
- Find the hypotenuse of this isosceles right triangle.
Using the formula c² = a² + b², we calculate the hypotenuse c = √2.
2.4 Combining two different squares
- What if we wish to combine two squares of different sizes to make a large square whose area is the sum of the two smaller squares?
Baudhāyana’s method uses the diagonal of a right triangle formed by the sides of the two squares to form the larger square.
2.5 Right-triangles having integer sidelengths
- List all the Baudhāyana triples with numbers less than or equal to 20.
The Baudhāyana triples include (3, 4, 5), (6, 8, 10), (9, 12, 15), (12, 16, 20).
- Is (30, 40, 50) a Baudhāyana triple?
Yes, it is a scaled version of the (3, 4, 5) triple.
2.6 A long-standing open problem
- Fermat’s Last Theorem states that there are no solutions to the equation xⁿ + yⁿ = zⁿ for n > 2. It was proven by Andrew Wiles in 1994.
2.7 Further applications of the Baudhāyana-Pythagoras theorem
- The Baudhāyana-Pythagoras theorem is applied in real-world problems, such as finding the depth of a lake and solving geometry puzzles.
Why NCERT solutions help students?
NCERT solutions provide exam readiness by offering clear and reliable answers that align with NCERT guidelines. These solutions help students build concept clarity, allowing them to confidently solve problems and gain a deeper understanding of geometric concepts.
Help your child build strong Mathematics fundamentals with expert-guided learning support.