1 / 8

Year 9 Similarity

This resource explores the key concepts of similarity and congruence in geometric shapes. Congruent shapes are identical in size and shape (including flipping), while similar shapes maintain the same shape but may differ in size. Through various examples and exercises, students learn to find missing side lengths in similar figures using proportional reasoning and the Pythagorean theorem. The document also includes challenges involving inscribed squares and highlights the unique properties of sizes of paper, enhancing geometric understanding.

riva
Télécharger la présentation

Year 9 Similarity

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related