Pythagoras’ Theorem

Students are guided through the discovery of Pythagoras’ Theorem using Pythagorean Triples.  They use Pythagoras’ Theorem to find the hypotenuse and shorter side of any right-angled triangle.  As learning progresses they begin to find lengths in 3D shapes.

Pythagoras’ Theorem takes place during    and  for Higher. This is the prerequisite for Trigonometry at both Foundation and Higher levels.


Pythagoras’ Theorem Lessons
Revision Lessons


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 three sides of a right angled triangle are connected by the areas of shapes on each edge. 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 by 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 squares in order for a2 + b2 = c2 to apply. In fact, the formula applies for 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.

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