1. Parallel Lines and Proportional Parts
Advanced Geometry

2. 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. Find x

4. Find x

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.

6. What does x have to be in order for ST to be parallel to QR?

7. Proportional Parts of Parallel Lines
If three parallel lines intersect two transversals, then they divide the transversals proportionally.

8. Lines k, m, and n are parallel and AB = 30.
Example
Lines k, m, and n are parallel and AB = 30.

9. Congruent Parts of Parallel Lines
If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

10. Find x and y

11. Find x