1. Chapter 7 Lesson 4: Parallel Lines and Proportional Parts Geometry CP Mrs. Mongold

2. Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional length. 3 4 6 x

3. Example Find x E H F L G 9 6 21 x

4. Converse of the Triangle Proportinoality Theorem If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side 10 5 12 6 *If the sides are proportional then the lines are parallel! So AB || DC A B D C

5. Triangle Midsegment Theorem A midsegment of a triangle is parallel to one side of the triangle and its length is one half the length of that side. A B C D E BC is congruent to BA AB is congruent to DE So BD= ½ AE

6. Find x and y 3x - 4 6 – 2x y + 1 3y

7. Find x and y 2x + 2 3x - 4 y + 7 5y

8. Find x and y 6y - 2 3y + 5 2x + 13x - 5

9. 7-4 Homework Pg 28/ 1-6 Pg 29/1-6