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MA28-12 Maths Coming soon

Using vectors to prove geometric results (Higher)

MA28-12

This lesson is coming soon.

In this lesson

Use vector expressions to show that two lines are parallel, that three points are collinear, or to solve a ratio/similarity problem, and write a complete concluding statement for the proof.

What it covers

  • Expressing two vectors (e.g. two sides, or two diagonals) in terms of given vectors using the route method
  • Recognising that one vector is a scalar multiple of another as evidence the corresponding lines are parallel
  • Recognising a shared point plus a scalar-multiple relationship as evidence of collinearity
  • Using a scalar-multiple relationship to solve a ratio or similarity problem within the diagram
  • Writing a complete, explicit concluding statement (e.g. 'AC = 2 x BD, so AC is parallel to BD' or 'since B lies on both AD and shares point A, A, B and D are collinear')

Key words

For: AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, OCR GCSE J560, Edexcel IGCSE 4MA1, Cambridge IGCSE 0580

On the specification

BoardSpecStatement
AQA GCSE 8300G25Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors
Edexcel GCSE 1MA1G25Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors
Eduqas GCSE C300HG25Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; use vectors to construct geometric arguments and proofs
OCR GCSE J5609.03aUnderstand addition, subtraction and scalar multiplication of vectors.
Edexcel IGCSE 4MA1H5.1GApply vector methods for simple geometrical proofs
Cambridge IGCSE 0580C7.4Extended content only.
Cambridge IGCSE 0580E7.4Represent vectors by directed line segments.
For teachers

This GCSE Maths lesson teaches using vectors to prove geometric results (Higher). By the end, students should be able to use vector expressions to show that two lines are parallel, that three points are collinear, or to solve a ratio/similarity problem, and write a complete concluding statement for the proof. It works through two worked examples and the mistakes examiners report.