Pythagoras' Theorem

Overview

The programme shows how Pythagoras’ Theorem can be used to find unknown lengths in right-angled triangles and to prove that a triangle is right-angled. It draws on the history of mathematics to show how this important theorem has been used for thousands of years to solve practical problems. Ben and Katie explore the relevance of Pythagoras’ Theorem in our own world, witnessing the construction of an aerial slide by the army, the positioning of equipment at a wind farm, and measurement of a corner on a football pitch. We see how to:

• express Pythagoras’ Theorem both algebraically and geometrically
• find the length of the hypotenuse of a right-angled triangle
• work with squares and square roots
• use the converse of the theorem to prove that a triangle is right-angled
• rearrange the formula to change the subject of the equation
• calculate the length of a shorter side of a right-angled triangle

The programme aims to enhance students’ understanding of the topic by providing clear visual explanations, dynamic geometrical demonstrations, and relevant applications from the real world.

The content is linked to the requirements of GCSE Intermediate Mathematics. It includes tips for answering exam questions, and a discussion of a typical exam error (‘Tick or Trash’). Relevant calculator functions are shown explicitly, but knowledge of the squares of whole numbers is also used to perform calculations mentally.

If students have covered the content elsewhere, the programme could be used to review the techniques and facts and provide meaningful contexts. It can be used either as a revision tool or to enrich other work on the topic. It could be shown in short sections to support students’ progress through stages of the work, and then be shown in full to summarise the topic. Students new to the topic would benefit from some introductory practical or investigative work before watching the programme.