Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

Exercises from Illustrative Mathematics A set of 2 exercises, commentary, and solutions

Students understand that the Ratio and Parallel Methods produce the same scale drawing and understand the proof of this fact.

Students relate the equivalence of the Ratio and Parallel Methods to the Triangle Side Splitter Theorem: A line segment splits two sides of a triangle proportionally if and only if it is parallel to the third side.

Teacher and Student versions of full lesson from engageNY

What if you were given a triangle with a line segment drawn through it from one side to the other? How could you use information about the triangle's side lengths to determine if that line segment is parallel to the third side? After completing this Concept, you'll be able to answer questions like this one.

Lessons, videos, exercises, and text from CK-12. Additional resources available at this site.