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Year 9 Similarity

Year 9 Similarity. Dr J Frost (jfrost@tiffin.kingston.sch.uk) . Last modified: 29 th October 2013. Similarity vs Congruence. Two shapes are congruent if:. !. ?. They are the same shape and size (flipping is allowed). Two shapes are similar if:. !. ?. They are the same shape

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Year 9 Similarity

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  1. Year 9Similarity Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 29th October 2013

  2. Similarity vs Congruence Two shapes are congruent if: ! ? They are the same shape and size (flipping is allowed) Two shapes are similar if: ! ? They are the same shape (flipping is again allowed) b b b a a a

  3. Similarity These two triangles are similar. What is the missing length, and why? 5 ? 7.5 8 12 There’s two ways we could solve this: The ratio of the left side and bottom side is the same in both cases, i.e.: We scale each length by the same amount. i.e.:

  4. Quickfire Examples Given that the shapes are similar, find the missing side (the first 3 can be done in your head). 1 2 10 12 ? 32 ? 24 18 15 15 20 4 17 3 24 11 20 40 25.88 25 ? ? 30

  5. Harder Problems (both these questions were on past landmarks) The diagram shows a square inside a triangle. DEF is a straight line. What is length EF? (Hint: you’ll need to use Pythag at some point) In the diagram BCD is similar to triangle ACE. Work out the length of BD. 2 1 Since EC = 12cm, by Pythagoras, DC = 9cm. Using similar triangles AEF and CDE: Thus ? ?

  6. Harder Problems 3 A square is inscribed in a 3-4-5 right-angled triangle as shown. What is the side-length of the square? 4 5 3 Work out the length of: a) b) 4 Suppose the length of the square is . Then . Then solve. ? so so . So Many students didn’t realise that the triangle on the left gets flipped upside down on the right, hence got an incorrect answer of for . ?

  7. Exercises A swimming pool is filled with water. Find . 1 2 3 ? ? ? 5 4 ? ?

  8. A4/A3/A2 paper “A” sizes of paper (A4, A3, etc.) have the special property that what two sheets of one size paper are put together, the combined sheet is mathematically similar to each individual sheet. What therefore is the ratio of length to width? A3 A4 So the length is times greater than the width. ? A3

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