1. Parallel Lines & Proportional Parts
Section 6-4

2. Thm. 6.4 Triangle Proportionality
If a line is parallel to one side of a triangle and intersects the other 2 sides in 2 distinct points, then it separates these sides into segments of proportional lengths.

3. x a y b

4. Theorem 6.5 (Converse of the Triangle Proportionality Thm.)
If a line intersects 2 sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the 3rd side.

5. 6.6 Triangle Midsegment Theorem
A midsegment of a triangle is parallel to one side of the triangle, and its length is 1/2 the length of that side.

6. A B D C
AB = ½ CD

7. Corollary 7-1 and 7-2
If 3 or more parallel lines intersect 2 transversals, then they cut off the transversals proportionally.
If 3 or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

8. b a c d

9. Joke Time
How would you describe a frog with a broken leg?
Unhoppy

10. What did the horse say when he got to the bottom of his nose bag?
That’s the last straw!