1. Use Proportionality Themes
Ch 6.6

2. Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other 2 sides, then it divides the 2 sides proportionally.
„RQS ~ „RTU

3. Converse of the Triangle Proportionality Theorem
If a line divides 2 sides of a triangle proportionally, then it is parallel to the third side.

4. Are the triangles similar? Can we find the length of QR?
yes
6x = 36
x = 6

5. Are the triangles similar? Can we find the length of all the sides?
yes
360 = 24x
x = 15

6. Find the length of x that makes these 2 triangles similar.

7. Find AB, FC, FE, and ED 8 7 6 10 12

8. Page 400 # 3 - 7

9. Theorem 6.6
If 3 parallel lines intersect 2 transversals, then they divide the transversals proportionally.

10. Theorem 6.7
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 2 sides.

11. Find the length of HG
150x = 36000
x = 240

12. Find the length of AB
8x = 60
x = 7.5

13. Find the length of the missing side.
4a = 18
x = 4.5

14. Find the length of the missing side.
3x = 28

15. Find the length of the missing side.
12a = 72

16. Find the length of the missing side
18 = 3x

17. Find the length of the missing side
18x = 72

18. Find the length of the missing side
3.5x = 27

19. Worksheet