In this lesson, students prove that a line parallel to one side of a triangle splits the other two sides proportionally. Along with the converse proven in an earlier lesson, students can now say that a line is parallel to one side of a triangle if and only if it splits the other two sides proportionally.

In proving the theorem in this lesson, students look for and make use of structure as they decide how they will prove that two triangles are similar (MP7).

Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.