1. Ratios and Scale Factors Slideshow 33, Mathematics Mr. Richard Sasaki, Room 307

2. Objectives Understand how to find and use the Ratio of Lengths and Ratio of Areas for given shapes Be able to find the value (weight) of a ratio Be able to find missing edges of similar triangles with the use of ratios Be aware that ratios can be formed for similar triangles in more than one way

3. Starting Exercise Easy exercise time! Find the unknowns in the equations with ratios. The solutions are shown in red.

4. Ratios of Different Properties Have a look at the two rectangles below. How do their sizes differ? We can either consider their areas or their dimensions (length and width). Ratio of Lengths: Ratio of Areas: We can use these to calculate missing lengths. Also, Ratios of Volume exist for 3D shapes. A B C D Note: These ratios are different to scales! M N P Q X Y

5. Answers

6. Scale Factors and Ratio Values Here are two similar ideas with inverse principles. If we look at the Ratio of Lengths for the two squares, we get. What is a Scale Factor? Scale Factors are an enlargement of one shape to another (a transformation). Scale factors consider lengths, not areas. Exactly 1The same size as the original. Less than 1The shape has shrunk. More than 1 The shape has grown. 1

7. Answers Scale Factor: 3 Next, let’s try the ActivExpression exercise!

8. Finding lengths with Ratios and Proportion Once again, for two shapes to be similar, they must… Have the same angles as one another Have lengths in the same proportion to each other The lengths must be in corresponding places (in terms of the angles for this to work. We could only complete a question like this with the sine or cosine rule. Let’s do questions where angles and lengths are in the same place!

9. Finding lengths with Ratios and Proportion The calculations are the same as last year, but this year, we must use ratios. Look at the two shapes below. We can say. Look at the two shapes below. Using the Ratio of Lengths, the equations for similarity are… or (or vice-versa). Using the first, we can say which implies that.

10. Finding lengths with Ratios and Proportion Example Look at the two similar rectangles below. Equation:

11. Answers For questions 1 – 6, you must show ratios in your calculations. Any possible ratios are fine.