1. Agenda 1) Bell Work 2) Outcomes 3) Finish 8.4 and 8.5 Notes 4) 8.6 -Triangle proportionality theorems 5) Exit Quiz 6) Start IP

2. Bell Work 1) Are the triangles similar? If so, explain why. 2) Solve for the missing variable a) b) 3) Write a statement of proportionality for the similar figures below:

3. Outcomes I will be able to: 1) Use ratios and proportions to find missing side lengths of similar figures 2) Understand intersections of parallel lines and triangles 3) Use proportionality theorems to find missing lengths

4. Socrative Student Review 1) Are the following triangles similar? A) Yes, by AA B) Yes, by SAS C) Yes, by SSS D) not similar

5. Socrative Student Review 2) Solve for the missing variable if the figures are similar. A) 10 B) 12 C) 14 D) 20

6. Socrative Student Review 3) Are the following triangles similar? A) Yes, by AA B) Yes, by SAS C) Yes, by SSS D) not similar

7. Socrative Student Review 4) Solve for the missing variable if the figures are similar. A) 15 B) 30 C) 36 D) 40

8. Socrative Student Questions 5) Write a statement of proportionality if the figures are similar. A) B)ABCD ~ MNOP C) D)

9. Proportions and Similar Triangles (8.6) Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. Meaning:

10. Proportions and Similar Triangles Converse of the Triangle Proportionality Theorem: If a line divides two sides of a triangle proportionally, then the line is parallel. Meaning: So, QS is parallel to TU

11. Example 4 2 2.5 x X = 3.2

12. On Your OWN Cross multiply: 200 = 200 So, yes, EB is parallel to DC 20 8 25 10 Use the converse of the triangle proportionality theorem.

13. Theorem 8.6 Theorem 8.6: If three parallel lines intersect two transversals, then they divide the transversals proportionally. Meaning:

14. Theorem 8.7 Theorem 8.7: If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other to sides Meaning:

15. Examples 2.4 1.4 2.2 x y z

16. On Your OWN Find the value of x 36 = 12x – 60 X = 8 How do we set this up?

17. Example x 14 - x How do we set this up?

18. On Your OWN Solve for p

19. Exit Quiz 1) Solve for the variable 2) Solve for the variable

20. IP Worksheet over triangle proportionality Due Friday Also, Friday, we will go over the quizzes from last week

21. Chapter 8 Review (Ratios) ***Remember, in order to have a ratio, we must make sure that each part of the ratio is in the same units Example: Remember to always move to the smallest unit

22. Chapter 8 Review (proportions) Remember, proportion rules If then… 1) Reciprocal property 2) 3)

23. Chapter 8 Review (geometric mean) Geometric mean: x = Example: Find the geometric mean of 6 and 8 x = = ***Remember to reduce (see board)

24. Chapter 8 Review (Similar Figures) Similar Figures must have congruent angles and side ratios that are proportional Similarity Statement: Statement of Proportionality

25. Chapter 8 Review (Similar Figures) Scale Factor: The ratio of corresponding sides in similar figures ***Used to find all the missing pieces in similar figures ***May be used to find the perimeter of similar figures See examples throughout notes

26. Chapter 8 Review (Similar Triangles) There are three ways to prove triangles are similar: AA – When you know two angles from the two triangles are congruent to each other Example: Each triangle has a right angle And vertical angles are congruent Triangles similar by AA

27. Chapter 8 Review (Similar Triangles) SSS – When all three side ratios are equal to each other Do these ratios equal each other? Yes, similar by SSS

28. Chapter 8 Review (Similar Triangles) SAS – When one angle is congruent and the side ratios of that included angle are equal to each other We know one angle is congruent. Check side lengths: Yes, similar by SAS