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
| Board | Spec | Statement |
|---|---|---|
| AQA GCSE 8300 | G25 | Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors |
| Edexcel GCSE 1MA1 | G25 | Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors |
| Eduqas GCSE C300 | HG25 | Apply 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 J560 | 9.03a | Understand addition, subtraction and scalar multiplication of vectors. |
| Edexcel IGCSE 4MA1 | H5.1G | Apply vector methods for simple geometrical proofs |
| Cambridge IGCSE 0580 | C7.4 | Extended content only. |
| Cambridge IGCSE 0580 | E7.4 | Represent 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.