1. Sect. 8.6 Proportions and Similar Triangles
Goal Use proportionality theorems to calculate segment lengths.
Goal Solve real-life problems, such as determining the dimensions of a piece of land.

2. Theorem 8.4 Triangle Proportionality Theorem
Using Proportionality Theorems
                                      
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. Theorem 8.5 Converse of the Triangle Proportionality Theorem
Using Proportionality Theorems
Theorem 8.5 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. Using Proportionality Theorems

5. Using Proportionality Theorems

6. Using Proportionality Theorems
                             
If three parallel lines intersect two transversals, then they divide the transversals proportionally.

7. Using Proportionality Theorems
                             
If a ray bisects an angle of a triangle, then it divides the opposite sides into segments whose lengths are proportional to the lengths of the other two sides.

8. Using Proportionality Theorems

9. Using Proportionality Theorems

10. Using Proportionality Theorems