1. Proportional Segments between Parallel Lines

2. Parallel Lines and Transversal
Alternate interior angles are congruent if the lines are parallel Corresponding angles are congruent if the lines are parallel Given the picture list all corresponding angles, list all Alternate interior angles (assume lines are parallel)

3. Parallel/Proportionality Conjecture
If a line parallel to one side of a triangle passes through the other two sides, then it divides the other two sides proportionally. (This ratio is not the scale factor between the triangles) Conversely, if a line cuts two sides of a triangle proportionally, then it is parallel to the third side.
Assume line is parallel to base of triangle

4. Example

5. Example

6. Extended Parallel/Proportionality Conjecture
If two or more lines pass through two sides of a triangle parallel to the third side, then they divided the two sides proportionally.

7. Example
Show that sides are divided proportionally, set up similar triangles and just proportional sides.

8. Homework
Pg odd Pg odd