1. Proportions and Similar Triangles
8.6

2. Theorem 8.4 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.

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

4. Example 1 4 8 12
In the diagram ll , BD=8,DC=4, and AE=12. What is the length of ?

5. Example 2
Given the diagram, determine whether
ll . 21 56 16 48

6. Find x.
36x = 840
x = 23⅓

7. Find x.
2(x + 6) = 5x
2x + 12 = 5x
-2x x
12 = 3x
4 = x

8. Find x. 2.5(8 – x) = 3.5x 20 – 2.5x = 3.5x +2.5x +2.5x 20 = 6x 6 6
3⅓ = x

9. Find x. 7 x
3x = 31.5 3
4.5
x = 10.5

10. Find x. 6(x + 5) = 10x 6x + 30 = 10x -6x -6x 30 = 4x 4 4 7.5 = x x 6
7.5 = x

11. Find x.
12.8x = 115.2
x = 9

12. Find x.
24x = 240
x = 10 in.

13. Find x.
12x = 72
x = 6 ft.

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

15. Example

16. 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 two sides.

17. Example
14-x x