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Benchmark Review

Explore the concept of similar figures, scale factor, and variation equations with questions and answers in this Geometry review. Understand how angles, sides, perimeters, and areas change based on scale factors. Learn about direct and inverse variation equations and identify patterns in ordered pairs.

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Benchmark Review

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  1. Benchmark Review 3rd Quarter

  2. If 2 figures are similar… 1. Their angles must be… 2. Their sides must be…

  3. Corresponding parts… • Triangles ABC and DEF are similar. 3. Which angles are corresponding? 4. Which sides are corresponding?

  4. Similar figures 5. If a rectangle has two sides that each measure x cm and two sides that each measure 5 cm more than the others, how can I find the perimeter?

  5. Scale Factor 6. If (16, 24) is dilated and the result is (8, 12), what is the scale factor? 7. If (10, 8) is dilated by a scale factor of 200%, what is the new ordered pair?

  6. Scale Factor 8. If a triangle with an area of 4 square cm is dilated to an area of 400 square cm, what is the scale factor?

  7. Scale Factor 9. How does the scale factor affect the perimeter of two figures?

  8. Scale Factor 10. How does the scale factor affect the area of two figures?

  9. Scale Factor 11. Two rectangles are similar. The side of the first one measures 15 cm. The side of the second one measures 50cm. What is the ratio of their areas?

  10. Scale Factor 12. The height of triangle 1 is 10cm and the height of triangle 2 is 20cm. What is the ratio of the areas of triangle 1 to triangle 2?

  11. Scale Factor 13. Scale factor that is less than 1 will do what to a figure? 14. Scale factor that is greater than 1 will do what to a figure? 15. Scale factor that is equal to 1 will do what to a figure?

  12. Variation… • What is the equation for direct variation? 17. What is the equation for inverse variation?

  13. Variation… • Does the following set of ordered pairs represent a direct variation, inverse variation, or neither? (1, 8) (2, 4) (4, 2) (8, 1)

  14. Variation… 19. Does the following set of ordered pairs represent a direct variation, inverse variation, or neither? (2, 4) (3, 6) (4, 8) (5, 10)

  15. Variation… 20. Does the following set of ordered pairs represent a direct variation, inverse variation, or neither? (1, 2) (2, 3) (3, 4) (4, 5)

  16. Variation… • If x varies directly with y, and x=5 when y=25, find y when x = 8. 22. If x varies inversely with y, and x=6 when y=8, find y when x=12.

  17. ANSWERS… • Congruent • In proportion • A to D, B to E, C to F 5. 4x + 10 6. ½ or .5

  18. ANSWERS CONTINUED… • (20, 16) • 10 • The same as the sides. • By the square of the scale factor

  19. ANSWERS CONTINUED… • Reduce • Enlarge • Congruent • 17. 18. Inverse 19. Direct • Neither • y=40 22. y=4

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