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  1. Glossary
  2. /Mathematics
  3. /Pythagoras Theorem

What is Pythagoras Theorem?

In short

Pythagoras' theorem says that in a right-angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides: c2=a2+b2c^2 = a^2 + b^2c2=a2+b2.

In simple words

The hypotenuse is the longest side, opposite the right angle. The converse is also true: if the sides satisfy c2=a2+b2c^2 = a^2 + b^2c2=a2+b2, the triangle has a right angle. Common whole-number triples are 3,4,53, 4, 53,4,5 and 5,12,135, 12, 135,12,13. The theorem is used to find a distance in the coordinate plane, as in the distance formula.

Example

A ladder 5 m5\ \text{m}5 m long leans on a wall with its foot 3 m3\ \text{m}3 m from the wall. The height reached is 52−32 m=4 m\sqrt{5^2 - 3^2}\ \text{m} = 4\ \text{m}52−32​ m=4 m.

Learn it properly

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Related terms

  • Isosceles Triangle
  • Trigonometric Ratios

← All glossary terms

Learn it in

  1. Congruent Triangles and Their PropertiesClass 9 to 10
  2. Similar Triangles and the Basic Proportionality TheoremClass 9 to 10
  3. Criteria for Similarity, Areas and the Pythagoras TheoremClass 9 to 10
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Practise

  1. Triangle ABC has sides BC = 36, CA = 29 and AB = 25…Advanced
A triangle ABC has sides a = BC, b = CA and c = AB…Advanced
  • In triangle ABC the sides are AB = 20, BC = 21 and CA = 13…Hard
  • A ladder 10 m long reaches 8 m up a wall…Hard
    • All problems on this topic →

    Quick questions

    1. In each statement, a, b, c are the sides of a triangle, Δ is its area and R is its…Advanced
    2. At noon an upright stick 1.5 m long casts a shadow 2 m long. A building next to it casts…Hard
    3. Triangles ABC and PQR are similar, and (ar(ABC))/(ar(PQR)) = 9/16. Which statement is…Hard

    More Mathematics terms

    1. Algebraic Identity
    2. Arithmetic Progression
    3. Complex Number
    4. Derivative
    5. Function
    6. Linear Equation
    All Mathematics terms →

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