Similar Polygons Unit : 6 - Section 7.3

Two polygons are similar if their vertices can be paired so that: 1.Corresponding angles are congruent. 2.Corresponding sides are proportional. (Their lengths have the same ratio. When referring to similar polygons, their corresponding vertices must be listed in the same order. If polygon PQRST is similar to polygon VWXYZ, you write polygon PQRST ∼ polygon VWXYZ. P S TR Q Z V Y W X 20 32

If polygon PQRST ∼ polygon VWXYZ. 1. ∠ P ∠ V ; ∠ Q ∠ W ; ∠ R ∠ X ; ∠ S ∠ Y ; ∠ T ∠ Z 2. Similarity is reflexive, symmetric, and transitive P S TR Q Z V Y W X 20 32

If polygon PQRST ∼ polygon VWXYZ, then the ratio of two corresponding sides is called the scale factor of the similarity. The scale factor of pentagon PQRST to pentagon VWXYZ is P S TR Q Z V Y W X 20 32

Example 1 : Quad. ABCD ∼ Quad. A’B’C’D’. Find: a.Their scales factor b.The values of x, y, and z x = 18, y = 20, and z = 13.2 c.The ratio of the perimeters 5:3 B C A A’ D B’ C’ D’ z x y

Practice 1 : Quad. EFGH ∼ Quad. E’F’G’H’. Find: a.Their scales factor 2:1 b.The values of x, y, and z x = 6, y = 6, and z = 5 c.The ratio of the perimeters 2:1 H G E E’ F H’ G’ F’ z x y

Practice 2: Quad. ABCD ∼ Quad. EFGH. Complete. a.m ∠ E = _____ b.m ∠ G = _____ c.m ∠ B = _____ d.If m ∠ D = 110, then m ∠ H = _____ e.The scale factor is _____ f.EH = ______ g.BC = ______ h.AB = ______ B C A F D G H E ° ° :3

Additional Practice: If time P. 250 #1-9 Homework: Practice Worksheet. 7.3