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Geometry Problems and Similar Polygons: Proportions and Ratios

Solve geometry problems using proportions and ratios. Learn to find unknown lengths in diagrams. Understand similar polygons, congruent angles, and scale factors to determine similarity. Practice calculating ratios and perimeters.

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Geometry Problems and Similar Polygons: Proportions and Ratios

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  1. 6.2 – Use Proportions to Solve Geometry Problems

  2. Complete the statement. y If , then x

  3. Complete the statement. x If , then y

  4. Complete the statement. 9+y If , then y

  5. Complete the statement. 5+11 If , then 11

  6. Use the given information and the diagram to find the unknown length. 3x = 2 2 3 x =

  7. Use the given information and the diagram to find the unknown length. 3x = 24 x = 8

  8. Use the given information and the diagram to find the unknown length. 18x = 180 x = 10

  9. Use the given information and the diagram to find the unknown length. 12x = 144 x = 12

  10. 6.3 – Use Similar Polygons

  11. Similar Polygons: • Corresponding angles are congruent • Corresponding sides are proportional

  12. Scale Factor: The ratio of the lengths of two corresponding sides of similar figures.

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

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

  15. Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor. Sides: Angles A  F B  D C  E

  16. Yes, they are similar. ABC ~ FDE Scale factor:

  17. Sides: Angles Q  W No, they are not similar. R  X S  Y T  Z

  18. The polygons are similar as noted. Find the value of x. 6x = 48 x = 8

  19. The polygons are similar as noted. Find the value of x. BCED ~ KLMJ 8x = 144 x = 18

  20. The two triangles are similar. Find the values of the variables. 6m = 66 m = 11

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

  22. 5. 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 6 4 Scale Factor: They are the same! Ratio of Perimeters:

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

  24. 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. 2x = 112 16 x = 56in x 2 7

  25. 7. In the diagram, WXYZ ~ BCDE. • Find the scale factor of WXYZ to BCDE.

  26. 7. In the diagram, WXYZ ~ BCDE. b. Find the values of XY and YZ. 4.5 4.5 2XY = 9 XY = 4.5

  27. 7. In the diagram, WXYZ ~ BCDE. b. Find the values of XY and YZ. 9 4.5 4.5 2XY = 9 2YZ = 18 XY = 4.5 YZ = 9

  28. 7. In the diagram, WXYZ ~ BCDE. c. Find mC. 9 mC = 117° 4.5 4.5

  29. 7. In the diagram, WXYZ ~ BCDE. d. Find the perimeter of WXYZ. 9 9 + 4.5 + 4.5 + 6 4.5 4.5 24u

  30. HW Problem 6.3 # 12 60 x x = 36in 3 5

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