Pythagoras’ Theorem

Scheme of work: GCSE Foundation: Year 10: Term 5: Pythagoras Theorem

Prerequisite Knowledge

  • derive and apply the properties and definitions of special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language
  • calculate the perimeters of 2D shapes, including composite shapes;
  • use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written description

Success Criteria

  • Know the formulae for Pythagoras theorem, a2 + b2 = c2
  • apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras Theorem and the fact that the
  • base angles of an isosceles triangle are equal, and use known results to obtain simple proofs

Key Concepts

  • Pythagoras’ Theorem identifies how the areas of shapes on each edge connect the three sides of a right-angled triangle. To fully engage with this concept, students could construct the theorem using a 3,4,5 triangle to measure the hypotenuse and calculate the area of each square. Their hypothesis can then be tested on a 5, 12, 13 triangle.
  • Pythagoras’ Theorem can be applied to a wide variety of geometrical and real world problems. Students need to practise identifying when the theorem can be applied by recognising triangular components.

Common Misconceptions

  • Students often believe that the areas of the shapes on the edges have to be squared for a2 + b2 = c2 to apply. The formula applies to all shapes as long as the dimensions are in proportion to the edges of the triangle.
  • Confusion often lies in identifying the Hypotenuse side of a right-angled triangle since it is not always apparent which side is longest. Encourage students to identify the hypotenuse as opposite the right angle.
  • There is often difficulty when trying to calculate a shorter side of a triangle since students tend to memorise the formula with the hypotenuse as the subject.

Pythagoras Theorem Resources

Mr Mathematics Blog

Problem-Solving with Angles in Polygons

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The Sum to Infinity of Geometric Series – A-Level Maths Tutorial

Explore geometric series in our A-Level Maths tutorial. Perfect for students/teachers, with resources to download at mr-mathematics.com.

Sequences and Series

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods