Lesson 7.4: Parallel Lines and Proportional Parts
Parallel Lines and Proportional Parts
Triangle Proportionality Theorem
If a Line is parallel to one side of a Triangle and intersects the other two sides, then it divides those sides proportionally.
If DE ∥ BC in △ABC, where D is on AB and E is on AC, then: AD/DB = AE/EC.
Converse
If a Line divides two sides of a Triangle proportionally, then it is parallel to the third side.
Midsegment Theorem
The segment connecting the midpoints of two sides of a Triangle is:
- Parallel to the third side.
- Half the length of the third side.
Corollary: Three Parallel Lines
If three or more parallel lines cut two transversals, they divide the transversals proportionally.