1. Then/Now You used proportions to solve problems. Use proportions to identify similar polygons. Solve problems using the properties of similar polygons.

2. Vocabulary similar polygons scale factor

3. Concept

4. Example 1 Use a Similarity Statement If ΔABC ~ ΔRST, list all pairs of congruent angles and write a proportion that relates the corresponding sides.

5. Example 1 Use a Similarity Statement Use the similarity statement. ΔABC ~ ΔRST Congruent Angles:  A   R,  B   S,  C   T Answer:

6. Example 1 If ΔGHK ~ ΔPQR, determine which of the following similarity statements is not true. A.  HGK   QPR B. C.  K   R D.  GHK   QPR

7. Example 3 Use Similar Figures to Find Missing Measures A. The two polygons are similar. Find x. Use the congruent angles to write the corresponding vertices in order. polygon ABCDE ~ polygon RSTUV

8. Example 3 Use Similar Figures to Find Missing Measures Write a proportion to find x. Similarity proportion Cross Products Property Multiply. Divide each side by 4. Simplify. Answer: x = __ 9 2

9. Example 3 Use Similar Figures to Find Missing Measures B. The two polygons are similar. Find y. Use the congruent angles to write the corresponding vertices in order. polygon ABCDE ~ polygon RSTUV

10. Example 3 Use Similar Figures to Find Missing Measures Similarity proportion Cross Products Property Multiply. Subtract 6 from each side. Divide each side by 6 and simplify. AB = 6, RS = 4, DE = 8, UV = y + 1 Answer: y = __ 3 13

11. Example 3 A.a = 1.4 B.a = 3.75 C.a = 2.4 D.a = 2 A. The two polygons are similar. Solve for a.

12. Example 3 A.1.2 B.2.1 C.7.2 D.9.3 B. The two polygons are similar. Solve for b.

13. Concept

14. Example 4 Use a Scale Factor to Find Perimeter If ABCDE ~ RSTUV, find the scale factor of ABCDE to RSTUV and the perimeter of each polygon.

15. Example 4 Use a Scale Factor to Find Perimeter The scale factor ABCDE to RSTUV is or. ___ AE VU __ 4 7 Write a proportion to find the length of DC. Since DC  AB and AE  DE, the perimeter of ABCDE is 6 + 6 + 6 + 4 + 4 or 26. Write a proportion. 4(10.5)= 7 ● DCCross Products Property 6= DCDivide each side by 7.

16. Example 4 Use a Scale Factor to Find Perimeter Use the perimeter of ABCDE and scale factor to write a proportion. Let x represent the perimeter of RSTUV. Theorem 7.1 Substitution 4x= (26)(7)Cross Products Property x= 45.5Solve.

17. Example 4 Use a Scale Factor to Find Perimeter Answer: The perimeter of ABCDE is 26 and the perimeter of RSTUV is 45.5.

18. Example 4 A.LMNOP = 40, VWXYZ = 30 B.LMNOP = 32, VWXYZ = 24 C.LMNOP = 45, VWXYZ = 40 D.LMNOP = 60, VWXYZ = 45 If LMNOP ~ VWXYZ, find the perimeter of each polygon.