Chapter Four Similarity

CHAPTER FOUR – SIMILARITY

LEARNING GOALS

· Understand that a scale factor measures the change in linear dimensions when you scale a picture.

· Approximate the scale factor relating two shapes by measuring. Use a scale factor to interpret a map or blueprint.

· Determine whether two figures are well-scaled copies of each other.

· Describe and use methods for constructing enlargements or reductions of shapes.

· Explain and contrast the ratio method the parallel method for dilation.

· Identify parallel segments and corresponding segments in a drawing and its scaled copy.

· Describe the effects of the choice for center of dilation on the resulting dilation.

· Investigate proportional relationships in nested triangles.

· Investigate how lines parallel to a side of a triangle cut the other two sides.

· Prove the side-splitter theorems.

· Identify invariants in dilations and enlargements.

· Identify corresponding parts of similar triangles.

· Develop and use the AA, SAS, and SSS tests for similarity in triangles.

· Understand the ratio between the area of a polygon and the area of a copy of that polygon scaled by the factor “r” will be r^2.