I saw this great monster GCSE question on Twitter (thanks @ReviseJustMaths) - it inspired me to write a post about similarity!

Taken from Edexcel Higher Paper 1 November 2013 |

In this post I'll focus on resources and methods for teaching

**similar triangles**.
Two triangles are similar if they're 'equiangular' (a bit of a mouthful so I teach 'AAA' instead). GCSE questions often require us to first match up equal angles before we start calculating unknown sides using ratio/proportional methods. This 'matching up' normally involves using angle rules - see my post on FUN angles. The key point to emphasise in teaching is that it really

**helps to draw the two triangles separately, and in the same orientation. Here's three examples to illustrate this:***really*Example 1 - Separate Triangles |

**Example 1**is straightforward - it's clear to see from the angle labels that the 8cm side in the first triangle is proportional to the side labelled x in the second triangle. I'd still encourage my pupils to redraw the two triangles in the same orientation though.

**Example 2**is less obvious. My pupils often make the mistake of thinking that side BC is proportional to side CE. I teach them to label all equal angles in the diagram, then draw triangles ABC and EDC separately. They'd then see that because <ABC = <CDE (alternate angles) and <ACB = <ECD (vertically opposite angles), the side BC is actually proportional to the side CD.

In

**Example 3**we can use the same approach as in Example 2. Label all the equal angles in the diagram ie <ABD = <ECD (corresponding angles), then draw the triangles ABD and ECD separately. In this question it's likely we'll be asked to work out the length BC, which just requires a bit of thinking (ie calculate the length BD first, then subtract the length CD).**Resources**

- I love these resources from the Mathematics Assessment Project. In particular, the sorting cards on pages 15 - 18 provide a challenging and engaging activity. I asked my pupils to sort the cards into three categories (similar/not similar/can't tell), stick them onto A3 paper and annotate with reasons.
- Similar pairs is a nice matching activity from Don Steward.
- This activity from Teach Mathematics has been tried by Mr Collins and reviewed in this blog post.
- This is a great booklet of practice questions. There's also some challenging questions in this worksheet from mathsmalakiss.com.
- CIMT has lots of excellent similarity resources.
- This is a lovely rich task from Shell Centre

For resources for area and volume of similar figures, see my resource library.

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