Copyright © 2014 Pearson Education, Inc. 5 CHAPTER 5.2 Similar Polygons Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Similar Polygons Similar polygons (figures) have the same shape but not necessarily the same size. We will abbreviate “is similar to” with the symbol ∼. Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Similar Polygons We write a similarity statement with corresponding vertices in order, the same way we write a congruence statement. When three or more ratios are equal, we can write an extended proportion. The proportion is an extended proportion. Copyright © 2014 Pearson Education, Inc.

Understanding Similarity and Using Extended Proportions a. What are the pairs of congruent angles? Use the order of the vertices in the similarity statement ΔMNP ∼ ΔSRT to write pairs of congruent angles. ∠M ≅ ∠S, ∠N ≅ ∠R, and ∠P ≅ ∠T Copyright © 2014 Pearson Education, Inc.

Understanding Similarity and Using Extended Proportions b. What is the extended proportion for the ratios of corresponding sides? Since ΔMNP ∼ ΔSRT, we know that corresponds to so is a ratio of corresponding sides the same is true for Copyright © 2014 Pearson Education, Inc.

Angle-Angle Similarity (AA ∼ ) Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Copyright © 2014 Pearson Education, Inc.

Using the AA ∼ Postulate Determine whether ΔRSW and ΔVSB are similar. Explain. Solution By studying the diagram, we see that we can use the AA ∼ Postulate. Show that two pairs of angles are congruent. ∠R ≅ ∠V because both angles measure 45°. ∠1 ≅ ∠2 because vertical angles are congruent. So, ΔRSW ∼ ΔVSB by the AA ∼ Postulate. Copyright © 2014 Pearson Education, Inc.

Using the AA ∼ Postulate Determine whether ΔJKL and ΔPQR are similar. Explain. Solution Look at the diagram, we see that we can use the AA ∼ Postulate. Show two pairs of angles congruent. ∠L ≅ ∠R because both angles measure 70°. m∠K = 180° − 30° − 70° = 80° m∠P = 180° − 85° − 70° = 25° Only one pair of angles is congruent. So, ΔJKL and ΔPQR are not similar. Copyright © 2014 Pearson Education, Inc.

Theorem 5.11 Triangle Prop. Theorem Theorem If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Triangle Prop. Theorem What is the value of x? Solution a side of triangle PMN. Set up a proportion using the Side-Splitter Theorem. Copyright © 2014 Pearson Education, Inc.

Transitive Law for Similar Triangles   Copyright © 2014 Pearson Education, Inc.