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.