Parallel Lines & Proportional Parts Section 6-4

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.

x a y b

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.

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.

A B D C AB = ½ CD

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.

b a c d

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

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