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

Vocabulary similar polygons scale factor

Concept

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

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

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

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

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

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

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

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.

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

Concept

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.

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 or 26. Write a proportion. 4(10.5)= 7 ● DCCross Products Property 6= DCDivide each side by 7.

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.

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

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.