1. Success Criteria:  Create proportion  Solve proportions Today’s Agenda Do now Check HW Lesson Check calendar for assignment Do Now: Chapter 7.2 Similar Polygons I can identify similar polygons and apply properties of similar polygons to solve problems. 1. If ∆QRS  ∆ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve the proportion. 2. Q  Z; R  Y; S  X; QR  ZY; RS  YX; QS  ZX x = 9

2. HW Answers

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

4. Let’s do a little review work before discussing similar figures.

5. Congruent Figures In order to be congruent, two figures must be the same size and same shape.

6. Similar Figures Similar figures must be the same shape, but their sizes may be different.

7. Similar Figures This is the symbol that means “similar.” These figures are the same shape but different sizes.

8. SIZES Although the size of the two shapes can be different, the sizes of the two shapes must differ by a factor. 33 2 1 6 6 2 4

9. SIZES In this case, the factor is x 2. 33 2 1 6 6 2 4

10. SIZES Or you can think of the factor as 2. 33 2 1 6 6 2 4

11. A similarity ratio is the ratio of the lengths of the corresponding sides of two similar polygons. The similarity ratio of ∆ABC to ∆DEF is, or. The similarity ratio of ∆DEF to ∆ABC is, or 2.

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

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

14. Describing Similar Polygons Find the similarity ratio and write the triangles similarity statement. N  Q and P  R. By the Third Angles Theorem, M  T. 0.5 What do you need to prove similarity??

15. Example 3: Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. ∆PQR and ∆STW

16. Example 3 Continued Step 1 Identify pairs of congruent angles. P  R and S  W isos. ∆ Step 2 Compare corresponding angles. Since no pairs of angles are congruent, the triangles are not similar. mW = mS = 62° mT = 180° – 2(62°) = 56°

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

18. 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

19. 70 40 We can verify this fact by placing the smaller triangle inside the larger triangle. 70 40

20. 70 40 The 40 degree angles are congruent.

21. 70 40 The 70 degree angles are congruent.

22. 70 40 4 The other 70 degree angles are congruent.

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

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

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

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

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

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

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

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

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

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

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

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

35. Similar figures “work” just like equivalent fractions. 5 30 66 11

36. These numerators and denominators differ by a factor of 6. 5 30 66 11 6 6

37. Two equivalent fractions are called a proportion. 5 30 66 11

38. Similar Figures So, similar figures are two figures that are the same shape and whose sides are proportional.

39. Practice Time!

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

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

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

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

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

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

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

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

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

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

50. Check calendar for assignment # pg 445 #21 (use pg 442 #3 as an example) Pg 445 #22,23,24 Pg 446 #32, 47

51. Success Criteria:  Create proportion  Solve proportions Today’s Agenda Do now Check HW Lesson Do Now: Chapter 7.2 Similar Polygons I can identify similar polygons and apply properties of similar polygons to solve problems. 1. Tell whether the following statement is sometimes, always, or never true. Two equilateral triangles are similar. Show or explain why. Always