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Contents Lesson 6-1Proportions Lesson 6-2Similar Polygons Lesson 6-3Similar Triangles Lesson 6-4Parallel Lines and Proportional Parts Lesson 6-5Parts of Similar Triangles Lesson 6-6Fractals and Self-Similarity

Lesson 2 Contents Example 1Similar Polygons Example 2Scale Factor Example 3Proportional Parts and Scale Factor Example 4Enlargement of a Figure Example 5Scale Factors on Maps

Example 2-1a Determine whether the pair of figures is similar. Justify your answer. Q The vertex angles are marked as 40º and 50º, so they are not congruent.

Example 2-1b Answer: None of the corresponding angles are congruent, so the triangles are not similar. Since both triangles are isosceles, the base angles in each triangle are congruent. In the first triangle, the base angles measure and in the second triangle, the base angles measure

Example 2-1c Determine whether the pair of figures is similar. Justify your answer. T Thus, all the corresponding angles are congruent.

Example 2-1d Now determine whether corresponding sides are proportional. The ratios of the measures of the corresponding sides are equal. Answer: The ratio of the measures of the corresponding sides are equal and the corresponding angles are congruent, so

Example 2-1e Determine whether the pair of figures is similar. Justify your answer. a.

Example 2-1e The ratio of the measures of the corresponding sides are equal and the corresponding angles are congruent, Answer: Both triangles are isosceles with base angles measuring 76º and vertex angles measuring 28º.

Example 2-1f Answer: Only one pair of angles are congruent, so the triangles are not similar. b. Determine whether the pair of figures is similar. Justify your answer.

Example 2-2a An architect prepared a 12-inch model of a skyscraper to look like a real 1100-foot building. What is the scale factor of the model compared to the real building? Before finding the scale factor you must make sure that both measurements use the same unit of measure. 1100(12) 13,200 inches

Example 2-2b Answer: The ratio comparing the two heights is The scale factor is, which means that the model is the height of the real skyscraper.

Example 2-2c A space shuttle is about 122 feet in length. The Science Club plans to make a model of the space shuttle with a length of 24 inches. What is the scale factor of the model compared to the real space shuttle? Answer:

End of Lesson 2

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