Pythagoras’ Theorem

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

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

For a right-angled triangle, Pythagoras Theorem states that a² +b² = c² where c is the hypotenuse.

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.

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

Geometry and measures
- Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagorasâ€™ 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.