Similarity

I saw this neat monster GCSE enquiry on Twitter (thanks @ReviseJustMaths) - it inspired me to write a postal service most similarity!

Taken from Edexcel Higher Paper ane Nov 2013

In this postal service I'll focus on resources as well as methods for didactics similar triangles.

Two triangles are similar if they're 'equiangular' (a flake of a mouthful thence I instruct 'AAA' instead). GCSE questions oftentimes require us to outset tally upwards equal angles earlier nosotros start calculating unknown sides using ratio/proportional methods.  This 'matching up' unremarkably involves using angle rules - come across my postal service on FUN angles. The cardinal betoken to emphasise inward didactics is that it truly really helps to describe the ii triangles separately, as well as inward the same orientation. Here's iii examples to illustrate this:

Example ane - Separate Triangles

Example 1 is straightforward - it's clear to come across from the angle labels that the 8cm side inward the outset triangle is proportional to the side labelled x inward the minute triangle.  I'd yet encourage my pupils to redraw the ii triangles inward the same orientation though.

Example 2 - Joined Triangles

Example 2 is less obvious.  My pupils oftentimes brand the error of thinking that side BC is proportional to side CE.  I instruct them to label all equal angles inward the diagram, thence describe triangles ABC as well as EDC separately. They'd thence come across that because <ABC = <CDE (alternate angles) as well as <ACB = <ECD (vertically contrary angles), the side BC is truly proportional to the side CD. 

Example 3 - Combined Triangles

In Example 3 we tin role the same approach every bit inward Example 2. Label all the equal angles inward the diagram ie <ABD = <ECD (corresponding angles), thence describe the triangles ABD as well as ECD separately. In this enquiry it's probable we'll endure asked to function out the length BC, which simply requires a flake of thinking (ie calculate the length BD first, thence subtract the length CD).  

Resources

• I dearest these resources from the Mathematics Assessment Project. In particular, the sorting cards on pages xv - eighteen furnish a challenging as well as engaging activity.  I asked my pupils to form the cards into iii categories (similar/not similar/can't tell), stick them onto A3 newspaper as well as annotate amongst reasons.  
• Similar pairs is a squeamish matching activeness from Don Steward.
• This blog post. 
• This is a great booklet of exercise questions. There's also closed to 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 expanse as well as mass of similar figures, come across my resource library.