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

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

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