Sectieoverzicht

  • Pythagoras was a Greek mathematician who is credited with one of the most famous theorems, which relates the sides of a right-angled triangle, called Pythagoras’ theorem. 

    Before you continue with Pythagoras’ theorem revise the basics you need to know about triangles by clicking on: Classifying triangles.

    A right-angled triangle has one \({90}^\circ\) angle. The longest side of the right-angled triangle is found opposite the right-angle and is called the hypotenuse (pronounced ‘high - pot - eh - news’). 

    Click where you see the "+" in the image below to learn more.

    In the next activity you will discover the Theorem of Pythagoras for yourself.

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      Discovering the theorem of Pythagoras

      In this interactive video activity you will be guided through the steps to discover Pythagoras' theorem for yourself.


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      What does Pythagoras' theorem say?

      In a right-angled triangle, a square formed on the hypotenuse will have the same area as the sum of the area of the two squares formed on the other sides of the triangle. 

      Geometrically the theorem can be shown as follows.

      Pythagoras Theorem

      The area of square A is equal to the sum of the areas of square B and C.

      Using a formula the theorem is stated as follows.

      Right-angled triangle ABC

      If \(\Delta ABC\) is right-angled at angle B then \({AC}^{2}={AB}^{2}+{BC}^{2}\) . 

      Conversely, if  \({AC}^{2}={AB}^{2}+{BC}^{2}\) then \(\Delta ABC\) is right-angled with \(\angle B={90}^\circ\) . 

      Remember the theorem of Pythagoras can only be used in a right-angled triangle.

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      Activity: Proving a triangle is right-angled