Pythagoras Theorem
Maharashtra Board · Class 10 · Mathematics
Quick revision notes for Pythagoras Theorem — Maharashtra Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
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Pythagoras Theorem - Basic Concept
- In a right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides
- The hypotenuse is always the longest side and is opposite to the right angle
- The theorem applies only to right-angled triangles (triangles with one 90° angle)
Converse of Pythagoras Theorem
- If in a triangle, the square of one side equals the sum of squares of other two sides, then it is a right triangle
- Used to verify if a triangle is right-angled when all three sides are known
- The side whose square equals the sum must be the hypotenuse
Pythagorean Triplets
- A set of three natural numbers where the square of largest equals sum of squares of other two
- Common examples: (3,4,5), (5,12,13), (8,15,17), (7,24,25)
- Any multiple of a Pythagorean triplet is also a Pythagorean triplet
Special Right Triangles
- 30°-60°-90° triangle: sides in ratio 1:√3:2
- 45°-45°-90° triangle: sides in ratio 1:1:√2
- Side opposite 30° = (1/2) × hypotenuse
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