Pythagoras’ Theorem and Right-Angled Triangles

Students are guided through the discovery of Pythagoras’ Theorem and learn how to apply it to calculate an unknown side in a right-angled triangle.  As learning progresses they are challenged to solve a range of problems using Pythagoras’ Theorem.

This unit takes place in Year 8 Term 6 and is follows finding the area of 2D and 3D shapes.


Pythagoras’ Theorem and Right-Angled Triangles Lessons
Problem Solving Lessons
Prerequisite Knowledge
  • Draw and measure line segments and angles in geometric figures, including interpreting scale drawings
  • Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
  • Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon
Key Concepts
  • For a right-angled triangle, Pythagoras’ Theorem states that a2 +b2 = c2 where c is the hypotenuse.
Pythagoras' Theorem and Right-Angled Triangles
  • A Pythagorean triple is a set of three integers that exactly fits the Pythagoras relationship.
  • If the lengths of the three sides of a triangle obey Pythagoras’ Theorem the triangle is right-angled.
  • Students should look for right-angled triangles in shapes with problem solving with Pythagoras’ Theorem.
Working mathematically

Develop fluency

  • Use language and properties precisely to analyse 2-D and 3-D shapes.
  • Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
  • Select and use appropriate calculation strategies to solve increasingly complex problems

Reason mathematically

  • Make and test conjectures about patterns and relationships; look for proofs or counter-examples
  • Begin to reason deductively in geometry, number and algebra, including using geometrical constructions

Solve problems

  • Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
  • Develop their use of formal mathematical knowledge to interpret and solve problems
  • Begin to model situations mathematically and express the results using a range of formal mathematical representations
  • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems
Subject Content

Geometry and measures

  • Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs
  • Use Pythagoras’ Theorem in similar triangles to solve problems involving right-angled triangles
  • Interpret mathematical relationships both algebraically and geometrically.

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