---
type: "Chapter"
knowledge_type: "chapter"
entity_type: "chapter"
id: "69c0d7398ef9305b088fded3"
title: "The Baudhayana-Pythagoras Theorem"
board: "CBSE"
curriculum: "CBSE"
class: "Class 8"
subject: "Mathematics"
book: "Ganita Prakash Part II"
chapter: "The Baudhayana-Pythagoras Theorem"
chapter_slug: "the-baudhayana-pythagoras-theorem"
canonical_url: "https://www.edzy.ai/cbse-class-8-mathematics-ganita-prakash-part-ii-the-baudhayana-pythagoras-theorem"
markdown_url: "https://www.edzy.ai/okf/chapter/cbse-class-8-mathematics-ganita-prakash-part-ii-the-baudhayana-pythagoras-theorem.md"
source_type: "examSubjectBookChapter"
source_id: "69c0d7398ef9305b088fded3"
source_pdf: "https://edzy-ai.s3.ap-south-1.amazonaws.com/edzy-express-ts/99fcb2a1-8800-4864-9868-083e8dde4570.pdf"
source: "Edzy"
version: 1
last_updated: "2026-06-20"
---

# The Baudhayana-Pythagoras Theorem
This chapter discusses the Baudhāyana-Pythagoras Theorem, showcasing various geometric constructions related to squares and the relationship between their areas through the guidance of Baudhāyana's ancient texts.

---

## Knowledge Snapshot

| Field | Details |
| :--- | :--- |
| Class | Class 8 |
| Subject | Mathematics |
| Book | Ganita Prakash Part II |
| Chapter | The Baudhayana-Pythagoras Theorem |
| Pages | 33-54 |

---

## Chapter Summary

### Short Summary
The chapter explores the Baudhāyana-Pythagorean theorem and its applications, detailing methods for constructing squares with double and half areas of given squares and understanding the relationships in isosceles right triangles.

### Detailed Summary
In this chapter, Baudhāyana's contributions to math in the context of constructing and calculating area through geometrical figures are examined. Key constructions include creating squares with double and half the area of original squares and applying the theorem to isosceles right triangles, leading to the concept that the sum of the squares of the sides is equal to the square of the hypotenuse.

---

## Topic-Wise Explanation

### Doubling a Square
Baudhāyana's Śulba-Sūtra addresses how to construct a square with double the area of a given square by creating a square on the diagonal of the original square.

### Halving a Square
The chapter explains how to draw a smaller square inside a larger one to achieve half the area of the original. This is shown through specific geometric methods using congruent triangles.

### Hypotenuse of an Isosceles Right Triangle
The length of the hypotenuse for an isosceles right triangle is established as $c = \sqrt{2}$ based on the relationship between the area of the square on the hypotenuse and the area of smaller squares formed by the triangle's sides.

### Combining Two Different Squares
Using the properties of right triangles, Baudhāyana describes how to combine two squares of different sizes to create a large square, affirming the relationship $a^2 + b^2 = c^2$.

### Right-Triangles Having Integer Sidelengths
Baudhāyana triples are introduced, showing that integer solutions to the equation $a^2 + b^2 = c^2$ include specific known sets such as (3, 4, 5) and (5, 12, 13).

### A Long-Standing Open Problem
The study of these triples raises questions leading to significant mathematical inquiries, including the nature of integer solutions for squared sums.

### Further Applications of the Baudhāyana - Pythagoras Theorem
This section examines practical problems and applications exemplified through Bhāskarāchārya's work, detailing various geometric scenarios adhering to the Baudhāyana theorem.

---

## Core Ideas

| Idea | Explanation |
| :--- | :--- |
| Baudhāyana's Theorem | The relationship $a^2 + b^2 = c^2$ for right triangles is unequivocally established, showcasing geometric evidence through practical constructions. |

---

## Key Concepts

| Concept | Meaning |
| :--- | :--- |
| Baudhāyana Triples | Integer solutions $(a, b, c)$ satisfying the equation $a^2 + b^2 = c^2$; e.g., (3, 4, 5). |
| Pythagorean Theorem | Fundamental theorem relating the lengths of the sides of a right triangle. |

---

## Important Points for Revision
* Baudhāyana established methods for constructing squares with specified areas.
* Diagonals play a critical role in doubling square areas.
* The Pythagorean theorem connects geometric constructs with algebraic identities.
* Baudhāyana triples illustrate integer relationships in right triangles.
* Applications of the theorem can be visualized through real-world problems.

---

## Vocabulary and Glossary

| Word / Phrase | Meaning |
| :--- | :--- |
| Baudhāyana | Ancient Indian mathematician known for his work in geometry. |
| Hypotenuse | The longest side of a right triangle opposite the right angle. |
| Isosceles Triangle | A triangle with at least two equal sides. |

---

## Practice Questions

### Short Answer Questions
1. What method does Baudhāyana propose to double the area of a square?
2. Calculate the hypotenuse of a triangle with equal sides measuring 1 unit each.
3. Identify three Baudhāyana triples that include numbers less than 20.
4. How can one construct a square equal to half the area of another square?
5. What property connects the sides of a right triangle?

### Long Answer Questions
1. Explain the process of combining two squares of different sizes to create a larger square using Baudhāyana's method.
2. Discuss the significance of the decimal representation of $\sqrt{2}$ and its implications for understanding integers and fractions.
3. Solve for the hypotenuse in a right triangle where the shorter sides are given lengths of 8 cm and 15 cm, using Baudhāyana's theorem.

---

## Related Concepts
* Integer point solutions in right triangles
* Geometric constructions in ancient mathematics
* Historical mathematicians and their contributions

---

## Source Attribution

| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 69c0d7398ef9305b088fded3 |
| Canonical URL | https://www.edzy.ai/cbse-class-8-mathematics-ganita-prakash-part-ii-the-baudhayana-pythagoras-theorem |
| Markdown URL | https://www.edzy.ai/okf/chapter/cbse-class-8-mathematics-ganita-prakash-part-ii-the-baudhayana-pythagoras-theorem.md |