Pythagoras Theorem | Class 8 Mathematics Notes
By ConceptScroll Team · Published on 17 July 2026 · 3 min read
Pythagoras Theorem – this guide gives you a concise, exam-ready overview of Pythagoras Theorem from Class 8 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.
Pythagoras Theorem
The Pythagoras Theorem formally states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Symbolically, if 'c' is the hypotenuse and 'a' and 'b' are the other two sides, then c² = a² + b². This theorem is fundamental in Euclidean geometry and is used to calculate distances and lengths in various geometric problems. The theorem can be proved using different methods, including geometric rearrangement and algebraic approaches. The NCERT textbook presents a proof using areas, which helps in visualizing the theorem. Understanding this theorem is crucial for solving problems involving right triangles and for further studies in trigonometry and coordinate geometry.
📊 Diagram: The diagram shows a right-angled triangle with sides labeled a, b, and c, where c is the hypotenuse. Squares are drawn on each side to represent their areas, visually demonstrating that the area of the square on the hypotenuse equals the sum of the areas of the squares on the other two sides.
🧪 Activity: No specific activity in this section, but the proof acts as a conceptual demonstration.
🔗 Connection: Prepares the student for the next section, which presents the proof of the theorem.
Frequently asked questions
1. Find the diagonal of a square with sidelength 5 cm.
The diagonal d of a square with side length a is given by the Pythagoras theorem: d = √(a² + a²) = √(2a²) = a√2. Here, a = 5 cm, so d = 5√2 cm ≈ 7.07 cm.
2. Find the missing sidelengths in the following right triangles: [The textbook shows several right triangles with some sides missing.]
Use the Pythagoras theorem a² + b² = c² where c is the hypotenuse.
For each triangle:
- Triangle with sides 4, 7, and missing side 10: Check if 4² + 7² = 10²? 16 + 49 = 65, 10²=100, no. So missing side must be calculated accordingly.
- Triangle with sides 9, 10, and missing side 41: Since 41 is large, likely hypotenuse.
- Triangle with sides 40, 45, and missing side 27: Calculate missing side using Pythagoras theorem.
- Triangle with sides 10, 150, and missing side 3: Check which is hypotenuse
3. Find the sidelength of a rhombus whose diagonals are of length 24 units and 70 units.
The diagonals of a rhombus bisect each other at right angles. Each side of the rhombus is the hypotenuse of a right triangle with legs half the diagonals.
Half diagonals: 24/2 = 12 units, 70/2 = 35 units.
Side length = √(12² + 35²) = √(144 + 1225) = √1369 = 37 units.
4. Is the hypotenuse the longest side of a right triangle? Justify your answer.
Yes, the hypotenuse is always the longest side of a right triangle. This is because, according to the Pythagoras theorem, the square of the hypotenuse equals the sum of the squares of the other two sides, so it must be longer than either of them.
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