Similarity
Friday, September 6, 2019
Edit
I saw this neat monster GCSE interrogation on Twitter (thanks @ReviseJustMaths) - it inspired me to write a postal service virtually similarity!
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| Taken from Edexcel Higher Paper 1 Nov 2013 |
In this postal service I'll focus on resources too methods for didactics similar triangles.
Two triangles are similar if they're 'equiangular' (a chip of a mouthful hence I learn 'AAA' instead). GCSE questions oft require us to kickoff jibe upward equal angles earlier nosotros start calculating unknown sides using ratio/proportional methods. This 'matching up' usually involves using angle rules - encounter my postal service on FUN angles. The primal betoken to emphasise inward didactics is that it genuinely really helps to depict the 2 triangles separately, too inward the same orientation. Here's 3 examples to illustrate this:
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| Example 1 - Separate Triangles |
Example 1 is straightforward - it's clear to encounter from the angle labels that the 8cm side inward the kickoff triangle is proportional to the side labelled ten inward the minute triangle. I'd withal encourage my pupils to redraw the 2 triangles inward the same orientation though.
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| Example 2 - Joined Triangles |
Example 2 is less obvious. My pupils oft brand the error of thinking that side BC is proportional to side CE. I learn them to label all equal angles inward the diagram, too hence depict triangles ABC too EDC separately. They'd too hence encounter that because <ABC = <CDE (alternate angles) too <ACB = <ECD (vertically reverse angles), the side BC is genuinely proportional to the side CD.
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| Example 3 - Combined Triangles |
In Example 3 we tin dismiss locomote the same approach equally inward Example 2. Label all the equal angles inward the diagram ie <ABD = <ECD (corresponding angles), too hence depict the triangles ABD too ECD separately. In this interrogation it's probable we'll live on asked to piece of occupation out the length BC, which simply requires a chip of thinking (ie calculate the length BD first, too hence subtract the length CD).
Resources
- I honey these resources from the Mathematics Assessment Project. In particular, the sorting cards on pages fifteen - xviii render a challenging too engaging activity. I asked my pupils to variety the cards into 3 categories (similar/not similar/can't tell), stick them onto A3 newspaper too annotate amongst reasons.
- Similar pairs is a squeamish matching activeness from Don Steward.
- This blog post.
- This is a great booklet of practise questions. There's also simply about challenging questions inward this worksheet from mathsmalakiss.com.
- CIMT has lots of first-class similarity resources.
- This is a lovely rich task from Shell Centre
For resources for surface area too mass of similar figures, encounter my resource library.
