Pythagoras’ Theorem

Scheme of work: Key Stage 3: Year 8: Term 6: Pythagoras Theorem

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 fit 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 formulating 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.

Pythagoras Theorem and Right-Angled Triangles Resources

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