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   Year 10 Term  and Year 9 Term 6 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.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Preparing Students for a Mathematics Exam

Preparing students for a mathematics exam takes time, patience and careful planning.  In this blog I will share my ideas for teaching students how to prepare for their final exams.  These are strategies that have worked well for me and I have see work well for others.  Creative writing to formulate ideas Students need space […]

Area of Compound Shapes

To find the area of compound shapes students need to understand what the word compound means.  Therefore, I ask students to discuss in pairs a definition for the word compound and to extend it to include the shapes below.  As a result of their learning in science students agree that a compound can be defined […]

Priorities for the Spring Term

At the start of the Spring Term these are three main priorities for me as the Head of Mathematics.