Schooling · Class 8 · Mathematics · The Baudhayana-Pythagoras Theorem · Chapter on a page
CBSE Class 8 · Mathematics · NCERT Ganita Prakash Part-II
The Baudhayana-Pythagoras Theorem: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- In a right-angled triangle, the side…
- The Baudhayana-Pythagoras Theorem…
- The converse is also true
- A Pythagorean triplet is a set of…
- If you multiply each number in a…
- The theorem works only for…
- Formulas and facts
- The Baudhayana-Pythagoras Theorem
- Finding the hypotenuse
- Finding a shorter side
- Test for a right-angled triangle
- Generating Pythagorean triplets
- Watch out for
- Using the theorem for triangles that…
- Adding all three squares instead of…
- Forgetting to take the square root…
- Identifying the wrong side as…
- Assuming any three numbers form a…
What this chapter is about
This chapter introduces one of the most important results in all of mathematics: the relationship between the sides of a right-angled triangle. Ancient Indian mathematician Baudhayana described this relationship in his Sulbasutras around 800 BCE, and Greek mathematician Pythagoras studied it later around 500 BCE. Both contributions are honoured in the chapter title.
Key ideas
- In a right-angled triangle, the side opposite the right angle is called the hypotenuse. It is always the longest side.
- The Baudhayana-Pythagoras Theorem states: In a right-angled triangle, (hypotenuse)² = (base)² + (height)², where base and height are the two sides forming the right angle.
- The converse is also true: If the square of one side of a triangle equals the sum of squares of the other two sides, the triangle must be right-angled.
- A Pythagorean triplet is a set of three positive whole numbers (a, b, c) where a² + b² = c². Common examples are (3, 4, 5), (5, 12, 13), (8, 15, 17) and (7, 24, 25).
- If you multiply each number in a Pythagorean triplet by the same whole number, you get another Pythagorean triplet. For example, multiplying (3, 4, 5) by 2 gives (6, 8, 10).
- The theorem works only for right-angled triangles. For other triangles, the relationship does not hold exactly.
Formulas and facts to remember
- The Baudhayana-Pythagoras Theorem:c² = a² + b²Here c is the hypotenuse, and a and b are the other two sides of a right-angled triangle.
- Finding the hypotenuse:c = √(a² + b²)Use this when you know both shorter sides and need the longest side.
- Finding a shorter side:a = √(c² − b²)Use this when you know the hypotenuse and one shorter side.
- Test for a right-angled triangle:If the three sides satisfy (longest side)² = (side 1)² + (side 2)², the triangle is right-angled.
- Generating Pythagorean triplets:For any whole number m greater than 1: the numbers (m² − 1), (2m), and (m² + 1) form a Pythagorean triplet.
Common mistakes
- Using the theorem for triangles that are not right-angled → First confirm there is a 90° angle before applying the formula.
- Adding all three squares instead of two → Only the two shorter sides are squared and added; the hypotenuse is squared alone on one side of the equation.
- Forgetting to take the square root at the end → After finding c² = 100, students sometimes write the answer as 100 instead of √100 = 10.
- Identifying the wrong side as hypotenuse → The hypotenuse is always opposite the right angle and is always the longest; check before substituting values.
- Assuming any three numbers form a Pythagorean triplet → Verify by calculation; for example, 3, 5, 7 do not satisfy 3² + 5² = 7² since 9 + 25 = 34 ≠ 49.
Quick revision
- In a right triangle: (hypotenuse)² = (base)² + (height)².
- The hypotenuse is opposite the 90° angle and is always the longest side.
- To test if a triangle is right-angled, check if the square of the longest side equals the sum of squares of the other two.
- (3, 4, 5), (5, 12, 13), and (8, 15, 17) are common Pythagorean triplets — memorise them for quick checks.
- Always take the square root after finding the square of the unknown side.