The chapter begins with an introduction to similar figures, followed by ways to prove triangles similar. The presence of proportional segments in similar figures is investigated. The second half of the chapter includes information on the lengths, areas, and volumes of similar figures; proportions relating to circles; and the fascinating Golden Ratio and its applications.

What you can expect to learn

After completing these activities you should be able to

  1. Define and identify similar figures.
  2. Solve proportions related to similar figures.
  3. State and apply the AA Similarity Postulate and the SSS and SAS Similarity Theorems.
  4. Prove and apply the Right Triangle Altitude Theorem and the geometric mean corollaries.
  5. Find the lengths of proportional partitions of triangles and transversals formed by parallel lines.
  6. Prove and apply theorems relating lengths, areas, and volumes of similar figures.
  7. Prove and apply theorems relating lengths of segments determined by chords, secants, and tangents within circles.
  8. Define the golden ratio and related figures.
Activity List