Geometric proofs with vectors
I can produce geometric proofs to prove that points are collinear or that vectors are parallel.
Geometric proofs with vectors
I can produce geometric proofs to prove that points are collinear or that vectors are parallel.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- Your knowledge of the properties of polygons can be applied to vector problems.
- A regular polygon has a relationship between sides that can be represented with vector notation.
- Your knowledge can be used to identify vectors and multiples of known vectors.
- Through manipulation, you can prove certain properties.
Keywords
Collinear - When three or more points lie on a single straight line, these points are said to be collinear.
Common misconception
When calculating the resultant vector, pupils can incorrectly sum vectors due to opposite directions or proportions of vectors.
Encourage pupils to write a clear vector pathway, sometimes using highlighters can help visualise this pathway.
To help you plan your year 11 maths lesson on: Geometric proofs with vectors, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Geometric proofs with vectors, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Vectors unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Starter quiz
6 Questions
AX : XB is 1 : 4 -
$$\frac{1}{5}\overrightarrow{AB}=\overrightarrow{AX}$$
AX : XB is 3 : 8 -
$$\frac{3}{11}\overrightarrow{AB}=\overrightarrow{AX}$$
AX : XB is 1 : 1 -
$$\frac{1}{2}\overrightarrow{AB}=\overrightarrow{AX}$$
AX : XB is 3 : 1 -
$$\frac{3}{4}\overrightarrow{AB}=\overrightarrow{AX}$$
$$x = 13$$ -
$${x \choose -2} + {12 \choose 7} = {25 \choose 5} $$
$$x=12$$ -
$${x\choose -7} + {-7 \choose -7} = {5 \choose -14} $$
$$x=4$$ -
$$x{2 \choose 8} = {8 \choose 32} $$
$$x=8$$ -
$$3{3\choose 4} + {3 \choose -4} = {12 \choose x} $$
Exit quiz
6 Questions
