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Geometry Review: Ratios, Proportions, and Similar Shapes

Solve geometry problems involving ratios, proportions, perimeters, and scaling factors with various triangles and shapes in this comprehensive review chapter.

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Geometry Review: Ratios, Proportions, and Similar Shapes

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  1. Chapter 7 Review

  2. A rectangle has sides in the ratio of 8 to 11. If the perimeter of a similar rectangle is 228, find the length of the longer side.

  3. ∆ABC ∼ ∆JKL, AB = 14, BC = 21.6, KL = 4.6, and JL = 3.3. Find the scale factor of ∆JKL to ∆ABC.

  4. Is trapezoid ABCD ∼ trapezoid PSRQ. Justify your answer.

  5. B C 11 E 3 6 A D 7 Find the length of BE.

  6. Identify the similar triangles by writing a similarity statement.

  7. Find MN.

  8. A dog and a puppy together weigh 39 pounds, with the ratio of their weights being 9 : 4. What is the weight of the puppy?

  9. If ∆FGH ∼ ∆JKL, find GX.

  10. Find the value of y.

  11. The ratio of the lengths of the sides of △ABC is 6 : 3.5 : 5 . The scale factor of ∆ABC to ∆DEC is 7 : 4, and the scale factor of ∆DEC to ∆FEG is 2 : 5. BC is the shortest side with a length of 10.5 and ABis the longest side of △ABC. Find FG.

  12. F x + 1 7 8 G K 12 x + 6 H J y Find the value of x.

  13. F x + 1 7 8 G K 12 x + 6 H J y Find the value of y.

  14. 8 2 6 x 16 y Find the value of x.

  15. 8 2 6 x 16 y Find the value of y.

  16. S R T 60 30 8 Find the ratio of the perimeter of ∆VSR to the perimeter of ∆TVR. 30 V

  17. S R T 60 30 8 Find the perimeter ∆SVR. 30 V

  18. A civil engineer is making a scale model of a highway on ramp. The length of the model is 4 inches. The actual length of the on ramp is 500 feet. a) What is the scale of the model? b) How many times as long as the actual on ramp is the model?

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