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Mastering Geometry: Ratios, Proportions & Similar Polygons

Learn how to write and reduce ratios, solve proportions, and determine similarity in polygons. Practice finding x and sides/angles in triangles. Discover AA, SAS, and SSS similarity criteria.

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Mastering Geometry: Ratios, Proportions & Similar Polygons

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  1. Chapter 7 Quiz Review Lessons 7.1-7.3

  2. You need to know: • How to write and reduce a ratio • How to write and solve a proportion • How to write a similarity statement, find a scale factor, and find x or y in a set of similar polygons • How to determine if two triangles or other polygons are similar and justify your answer (corresponding sides are proportional and corresponding angles are congruent or for triangles: AA Similarity, SAS Similarity, or SSS Similarity)

  3. 1a. Find x and the length of each side of the triangle. The three sides of a triangle are in the ratio 2:4:5. The perimeter of the triangle is 253cm.

  4. 1b. Find x and the length of each side of the triangle. The three angles of a triangle are in the ratio 4:5:6. Find the measure of each angle.

  5. 2. Solve the Proportion

  6. 3. Solve the Proportion

  7. 4. Determine if the polygons are similar. Write a similarity statement and find the scale factor.

  8. 5. Determine if the triangles are similar. Write a similarity statement, find the scale factor, and find x.

  9. 6. The quadrilaterals are similar, find x and CB.

  10. 7. Determine if the triangles are similar, justify your answer.

  11. 8. Determine if the triangles are similar, justify your answer.

  12. 9. Find x, AB and BC.

  13. 10. Find x, BC, and AC

  14. 1a. 2x + 4x + 5x = 253 11x = 253 x = 23 46cm, 92cm, 115cm 1b. 4x + 5x + 6x = 180 15x = 180 x = 12 48, 60, 72 degrees 2. 5x9 = 6(x + 2) 45 = 6x + 12 33 = 6x x = 5.5 Answers:

  15. 3. 6(x + 7) = 7(x + 4) 6x + 42 = 7x + 28 42 = x + 28 x = 14 4. Triangle ABC~Triangle EDF scale factor = 1/1 Answers:

  16. 5. Yes they are similar by AA Similarity. scale factor= 6. Answers:

  17. 7. Yes by SSS similarity. 8. Yes by SAS Similarity. (all corresponding sides are in a ratio of 1/1) Answers:

  18. 9. 10. Answers:

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