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Bell Ringer

Bell Ringer. 6. 7. Two polygons are similar polygons if corresponding angles are congruent and corresponding side length are proportional. Similar Polygons. Example 1. Use Similarity Statements.  PRQ ~  STU. a. List all pairs of congruent angles. b.

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Bell Ringer

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  1. Bell Ringer 6. 7.

  2. Two polygons are similar polygons if corresponding angles are congruent and corresponding side length are proportional. Similar Polygons

  3. Example 1 . . Use Similarity Statements PRQ ~ STU. a. List all pairs of congruent angles. b. Write the ratios of the corresponding sides in a statement of proportionality. 12 16 ST US US TU TU 8 ST 4 4 4 QP 20 15 10 RQ PR RQ QP PR 5 5 5 c. Check that the ratios of corresponding sides are equal. SOLUTION 4 The ratios of corresponding sides are all equal to 5 a. PS,RT,andQU. b. = = = = = = = = c. , , and

  4. If two polygons are similar, then the ratios of the lengths of the two corresponding sides is called the scale factor.

  5. Example 2 SOLUTION Determine Whether Polygons are Similar Determine whether the triangles are similar. If they are similar, write a similarity statement and find the scale factor of Figure B to Figure A. 1. Check whether the corresponding angles are congruent. From the diagram, you can see that G M,H  K, and J  L. Therefore, the corresponding angles are congruent.

  6. Example 2 All three ratios are equal, so the corresponding side lengths are proportional. By definition, the triangles are similar. GHJ ~ MKL. ANSWER 4 . The scale factor of Figure B to Figure A is 3 Determine Whether Polygons are Similar MK 12 12 ÷ 3 4 = = = GH 9 9 ÷ 3 3 KL 16 16 ÷ 4 4 = = = HJ 12 ÷ 4 3 12 20 LM 20 ÷ 5 4 = = = JG 15 ÷ 5 3 15 2. Check whether the corresponding side lengths are proportional.

  7. Now You Try  3 ANSWER yes;XYZ ~ DEF; 2 no ANSWER Determine Whether Polygons are Similar Determine whether the polygons are similar. If they are similar, write a similarity statement and find the scale factor of Figure B to Figure A. 1. 2. 12 9 ≠ 10 6

  8. Example 3 Use Similar Polygons RST ~ GHJ. Find the value of x. 9 GH JG 15 x RS TR 10 SOLUTION Because the triangles are similar, the corresponding side lengths are proportional. To find the value of x, you can use the following proportion. Write proportion. = Substitute 15 for GH, 10 for RS, 9 for JG, and x for TR. = 15 · x=10 · 9 Cross product property

  9. Example 3 Use Similar Polygons 15x =90 Multiply. 90 15x Divide each side by 15. = 15 15 x =6 Simplify.

  10. Example 4 Perimeters of Similar Polygons The outlines of a pool and the patio around the pool are similar rectangles. a. Find the ratio of the length of the patio to the length of the pool. 3 2 b. Find the ratio of the perimeter of the patio to the perimeter of the pool. SOLUTION a. The ratio of the length of the patio to the length of the pool is length of the patio 48 feet 48 ÷ 16 = = = . 32 ÷ 16 length of pool 32 feet

  11. Example 4 Perimeters of Similar Polygons b. The perimeter of the patio is 2(24) + 2(48) = 144 feet. The perimeter of the pool is 2(16) + 2(32) = 96 feet. The ratio of the perimeter of the patio to the perimeter of the pool is perimeter of patio 144 feet 144 ÷ 48 3 = = = . 2 96 ÷ 48 perimeter of pool 96 feet

  12. Now You Try  Use Similar Polygons In the diagram,PQR ~ STU. 3. Find the value of x. ANSWER 18 4. Find the ratio of the perimeter of STUto the perimeter of PQR. ANSWER 1 2

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