Pythagoras' Theorem

Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.

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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)

Write it as a² + b² = c², where c is the hypotenuse. It only works when one angle is exactly 90°.

Four copies of the triangle packed into a big square leave a c-square gap in the middle, and the algebra gives a² + b² = c².

Hypotenuse: c = √(a²+b²). Shorter side: a = √(c²−b²). Always spot the hypotenuse first - it faces the right angle.

This is the converse. Whole-number sets that work (like 3-4-5) are called Pythagorean triples.

hypotenuse	the longest side of a right-angled triangle, opposite the right angle
right angle	an angle of exactly 90°, shown by a small square in the corner
square (of a number)	a number multiplied by itself, written with a small ²
square root	the value that, multiplied by itself, gives the number; symbol √
Pythagorean triple	three whole numbers that satisfy a² + b² = c², such as 3-4-5
converse	the reverse statement: if a² + b² = c², the triangle is right-angled
space diagonal	the line through the inside of a cuboid joining opposite corners

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