1. Similar Figures (Not exactly the same, but pretty close!)

2. A dilation is when you create a similar figure that is larger or smaller than the original figure. Each side is multiplied by the same scale factor, so the new dilated shape is proportional to the original. 33 2 1 6 6 2 4 Dilations

3. Dilation: Englargement In this case, the scale factor is 2. 33 2 1 6 6 2 4

4. Enlargements When you have a photograph enlarged, you make a similar photograph. X 3

5. Reductions A photograph can also be shrunk to produce a slide. 4

6. Determine the length of the unknown side. 12 9 15 4 3 ?

7. These triangles differ by a factor of 3. 12 9 15 4 3 ? 15 3= 5

8. Determine the length of the unknown side. 4 2 24 ?

9. These dodecagons differ by a factor of 6. 4 2 24 ? 2 x 6 = 12

10. Sometimes the factor between 2 figures is not obvious and some calculations are necessary. 18 12 15 12 108 ? =

11. To find this missing factor, divide 18 by 12. 18 12 15 12 108 ? =

12. 18 divided by 12 = 1.5

13. The value of the missing factor is 1.5. 18 12 15 12 108 1.5 =

14. When changing the size of a figure, will the angles of the figure also change? ?? ? 70 40

15. Nope! Remember, the sum of all 3 angles in a triangle MUST add to 180 degrees. If the size of the angles were increased, the sum would exceed 180 degrees. 70 40 70 40

16. 70 40 We can verify this fact by placing the smaller triangle inside the larger triangle. 70 40

17. 70 40 The 40 degree angles are congruent.

18. 70 40 The 70 degree angles are congruent.

19. 70 40 4 The other 70 degree angles are congruent.

20. Find the length of the missing side. 30 40 50 6 8 ?

21. This looks messy. Let’s translate the two triangles. 30 40 50 6 8 ?

22. Now “things” are easier to see. 30 40 50 8 ? 6

23. The common factor between these triangles is 5. 30 40 50 8 ? 6

24. So the length of the missing side is…?

25. That’s right! It’s ten! 30 40 50 8 10 6

26. Similarity is used to answer real life questions. Suppose that you wanted to find the height of this tree.

27. Unfortunately all that you have is a tape measure, and you are too short to reach the top of the tree.

28. You can measure the length of the tree’s shadow. 10 feet

29. Then, measure the length of your shadow. 10 feet 2 feet

30. If you know how tall you are, then you can determine how tall the tree is. 10 feet 2 feet 6 ft

31. The tree must be 30 ft tall. Boy, that’s a tall tree! 10 feet 2 feet 6 ft

32. Similar Figures Similar figures are two figures that are the same shape and whose sides are proportional. Similar figures have congruent angles.

33. Practice Time!

34. 1) Determine the missing side of the triangle. 3 4 5 12 9 ? 

35. 1) Determine the missing side of the triangle. 3 4 5 12 9 15 

36. 2) Determine the missing side of the triangle. 6 4 6 36  ?

37. 2) Determine the missing side of the triangle. 6 4 6 36  24

38. 3) Determine the missing sides of the triangle. 39 24 33 ? 8  ?

39. 3) Determine the missing sides of the triangle. 39 24 33 13 8  11

40. 4) Determine the height of the lighthouse. 2.5 8 10  ?

41. 4) Determine the height of the lighthouse. 2.5 8 10  32

42. 5) Determine the height of the car. 5 3 12  ?

43. 5) Determine the height of the car. 5 3 12  7.2

44. THE END!