KS4 Pythagoras Worksheets

Pythagoras' theorem is introduced at KS4, typically in Year 10, as part of the geometry and measures strand of the National Curriculum. Year 11 students revisit the theorem during GCSE revision and encounter it embedded within more complex problems across various topics including trigonometry, vectors, and 3D shapes. Both foundation and higher tier students are expected to apply the theorem confidently.

The difficulty progression from Year 10 to Year 11 moves from isolated triangle problems with clearly labelled diagrams toward multi-step applications. By Year 11, students tackle problems where identifying that Pythagoras is needed becomes the first challenge, such as finding the perpendicular height of an isosceles triangle or calculating space diagonals in cuboids. Higher tier students must also work fluently with exact answers involving surds rather than calculator approximations.

The worksheets build systematically from identifying right-angled triangles and labelling sides correctly through to complex applications, allowing teachers to select sheets that match current teaching objectives. Starting with simpler problems where the triangle is clearly marked helps establish the formula before introducing questions where students must first spot which triangle to use. The answer sheets enable students to self-check during independent practice, encouraging them to identify and correct errors immediately rather than embedding misconceptions.

Many teachers use these worksheets for targeted intervention with students who struggle to transfer Pythagoras into problem-solving contexts, particularly those who can apply the formula in isolation but fail to recognise when it's needed. They work well as homework following initial teaching, as starters to maintain fluency during the run-up to exams, or for paired work where students explain their reasoning to each other. The variety of question types means teachers can differentiate easily within mixed-attainment groups.