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Unit 5 Lesson 2 Notes Use Similar Polygons

Learn about similar polygons and their properties, including congruent angles and proportional sides. Find the scale factor and solve for variables in similarity statements.

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Unit 5 Lesson 2 Notes Use Similar Polygons

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  1. Unit 5 Lesson 2 Notes Use Similar Polygons

  2. Similar Polygons: ~ • Corresponding angles are congruent • Corresponding sides are proportional

  3. Scale Factor: The ratio of the all of the sides of similar figures.

  4. 1. List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality. B  E A  D Angles: _______ _______ _______ Sides: ___________________ C  F

  5. 1. List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality. Angles: _______ _______ _______ _______ Sides: __________________________ C  M D  J E  K F  L

  6. Angles Sides ________ _______ ________ _______ ________ _______ Similar: YES or NO Similar Statement: ___________________ Scale Factor: ________ 2. Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor from triangle B to triangle A. P  M T  L O  N PTO ~ MLN

  7. Angles Sides ________ _______ ________ _______ ________ _______ Similar: YES or NO Similar Statement: ___________________ Scale Factor: ________ 2. Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor from triangle B to triangle A. B A

  8. 3. The polygons are similar. Find the values of the variables. 1 2 6x = 48 x = 8 x = 8

  9. 3. The polygons are similar. Find the values of the variables. 6m = 66 m = 11

  10. 3. The two triangles are similar. Find the values of the variables. 6m = 66 12n = 48 m = 11 n = 4

  11. 4. The two figures are similar. Find the scale factor of their sides. Then find the ratios of their perimeters. What do you notice? 18 12 12 8 36 24 6 4 Scale Factor: They are the same! Ratio of Perimeters:

  12. ratio If two polygons are similar, then the ______ of their __________ is equal to the ratios of their corresponding ____ lengths perimeters side

  13. 5. The ratio of one side of a picture to the corresponding side of a larger picture is 2:7. The perimeter of the smaller picture is 16 inches. Find the perimeter of the larger picture. 1 8 x 16 2x = 112 2 7 x = 56in x = 56in

  14. 6. In the diagram, WXYZ ~ BCDE. • Find the scale factor of WXYZ to BCDE.

  15. 6. In the diagram, WXYZ ~ BCDE. b. Find the value of XY. 3 4.5 4.5 2XY = 9 XY = 4.5

  16. 6. In the diagram, WXYZ ~ BCDE. c. Find mC. 3 mC = 117° 4.5 4.5

  17. 6. In the diagram, WXYZ ~ BCDE. d. Find the perimeter of WXYZ. 3 16 x 1 8 4.5 4.5 2x = 48 x = 24 x = 24

  18. Prove Triangles Similar by AA

  19. AA Similarity (AA ~) Two triangles are similar if two of their corresponding angles are congruent.

  20. Use the diagram to complete the statement. GHI

  21. Use the diagram to complete the statement. GI HI GH

  22. Use the diagram to complete the statement. x

  23. Use the diagram to complete the statement. 8

  24. Use the diagram to complete the statement. 5. x = _______ x 12x = 160 40 3 x =

  25. Use the diagram to complete the statement. 6. y = _______ 8 12y = 128 32 3 y =

  26. 7. Determine whether the triangles are similar. If they are, explain why andwrite a similarity statement. 77° 55° YES or NO Postulate: ______________ Similarity: _____________ AA~ ABC ~ DEF

  27. 7. Determine whether the triangles are similar. If they are, explain why andwrite a similarity statement. 47° YES or NO Postulate: ______________ Similarity: _____________ 31°

  28. 7. Determine whether the triangles are similar. If they are, explain why andwrite a similarity statement. YES or NO Postulate: ______________ Similarity: _____________ AA~ ABC ~ EDC

  29. 7. Determine whether the triangles are similar. If they are, explain why andwrite a similarity statement. YES or NO Postulate: ______________ Similarity: _____________ AA~ SRV ~ TRU

  30. 8. Find the length of BC. 7x = 20 20 7 x =

  31. 9. Find m. 1 3 70m = 13650 m = 195 m = 195

  32. 10. Find the value of x. 4x = 70 x = 17.5 x 5 14 4 10 4

  33. 10. Find the value of x. 8 8x = 56 8 x = 7 14 4 4 6 x x

  34. 11. In order to estimate the height, h, of a flag pole, a 5 foot tall male student stands so that the tip of his shadow coincides with the tip of the flag pole’s shadow. • a. Are the two triangles similar? Explain. AA ~ Yes,

  35. 11. In order to estimate the height, h, of a flag pole, a 5 foot tall male student stands so that the tip of his shadow coincides with the tip of the flag pole’s shadow. h 5 • b. Find the height, h, of the flag pole. 6 1 18 3 6h = 90 x = 15ft x = 15ft

  36. HW Problem FRONT PAGE # 11 12 n 27.5 P = 34 P = 85 2x = 55 2n = 15 5y = 60 n = 7.5 x = 27.5 y = 12

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