Topic outline

  • Outcomes

    Collapse all Expand all

    In this course you will learn about: 

    1. The relationship between the sides of a right-angled triangle.
    2. Using the Theorem of Pythagoras to find missing lengths in a right angled triangles. 

  • Sides of a right-angled triangle

    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.

    • Discovering the theorem of Pythagoras

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


    • 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.

    • Activity: Proving a triangle is right-angled




  • Using the theorem of Pythagoras

    You can use the Theorem of Pythagoras to find the lengths of missing sides if you know that a triangle is right-angled. The theorem of Pythagoras has many applications in Trigonometry. 

    In the next video you will see a worked example to calculate the length of an unknown side in a right-angled triangle. This example will help you complete the activity in the video. When you have completed the video try the activity that follows.