G-11 Similar Triangles I can demonstrate the equality of corresponding angles and proportionality of sides using similarity and similarity transformations.

Similar Figures Corresponding angles are congruent Corresponding sides are proportional Figures that are similar (~) have the same shape but not necessarily the same size.

A similarity ratio is the ratio of the lengths of the corresponding sides of two similar polygons. The similarity ratio of ∆ABC to ∆DEF is , or . The similarity ratio of ∆DEF to ∆ABC is , or 2.

Example 1a Identify the pairs of congruent angles and corresponding sides.

Example 1b Identify the pairs of congruent angles and corresponding sides.

Example 1c Identify the pairs of congruent angles and corresponding sides.

Example 2a Determine if ∆JLM and ∆NPS are similar. If so, write the similarity ratio and a similarity statement.

Example 2b Determine if the triangles are similar. If so, write the similarity ratio and a similarity statement.

Example 2c Determine if the triangles are similar. If so, write the similarity ratio and a similarity statement.

Example 3a A dining room is 18 ft long and 14 ft wide. On a blueprint for the house, the dining room is 3.5 in. wide. To the nearest tenth of an inch, what is the length of the dining room on the blueprint?

Example 3b A classroom is 30 ft long and 25 ft wide. On a blueprint for the school, the class is 7.3 in. long. To the nearest tenth of an inch, what is the width of the classroom on the blueprint?

Example 4 Solve each proportion. A. B. C. D.

Example 4 Solve each proportion. E. F.