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Understanding Proportions and Similar Polygons in Geometry

Explore key concepts of proportions, similar polygons, and the mathematical relationships between means and extremes. Discover the properties of similar shapes and the importance of ratios in geometry, all explained in an easy-to-understand manner.

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Understanding Proportions and Similar Polygons in Geometry

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  1. Chapter 8

  2. 2 34 6 ___ ___ = The means are _____ The extremes are ____

  3. Means: 3 and 4Extremes: 2 and 6

  4. In a proportion, the product of the _____ equals the product of the _____

  5. In a proportion, the product of the means equals the product of the extremes

  6. What symbol is used for “similar”?

  7. ~

  8. For similar polygons,corresponding angles are ____ andcorresponding sides are ____

  9. For similar polygons,corresponding angles are congruent andcorresponding sides are proportional

  10. If DOG ~ CAT then D ~ ___ and G ~ ____ = =

  11. If DOG ~ CAT then D C and G T ~ ~ = =

  12. Always, sometimes or never? Two congruent polygons are _____ similar

  13. Two congruent polygons are always similar

  14. Always, sometimes or never? Two rectangles are _____ similar

  15. Two rectangles are sometimes similar

  16. The ratio of the length:width of a Golden Rectangleis (approximately) _____ : _____

  17. The ratio of the length:width of a Golden Rectangleis (approximately)1.62 : 1

  18. If BAD ~ CAT thencomplete the proportion: B T z a x A b c y C D ab c = =

  19. a b cy x z = = ___ ___ ___

  20. Complete the proportion:34x = = 3 4 x y 8 15

  21. 34x = = 3 + y 12 15 (scale factor = 1:3) 3 4 x y 8 15

  22. Multiply (x + 3)(x – 5)

  23. (x + 3)(x – 5) = x2 – 5x + 3x – 15F O I L= x2 – 2x - 15

  24. SOLVE BY FACTORING:x2 – 9 = 0x2 + 3x –18 = 0

  25. x2 – 9 = 0 (x – 3)(x + 3) = 0 x = 3 or -3 x2 + 3x –18 = 0 (x + 6)(x – 3)= 0 x = -6 or 3

  26. Complete the proportion: __ __ = x 10 5

  27. __ __ 10 xx 5 = hyp1alt alt hyp2 _____ _____ =

  28. Complete the proportion: __ __ y = 10 5

  29. 10 y y 15 __ __ = hyp1leg1 leg1 hyp _____ _____ =

  30. Complete the proportion: __ __ = z 10 5

  31. 5 z z 15 __ __ = hyp2leg2 leg2 hyp _____ _____ =

  32. Find the Geometric Mean of 4 and 8

  33. 32 (4)(8) = 4 2 = (Square root of product)

  34. Complete the proportion:a b ___ ___ = y x a b

  35. a b x ___ ___ = y y x a b

  36. Complete the proportion:a b ? ___ = ___ ? a c b d

  37. a c ___ = ___ b d a c b d

  38. For similar polygons, the ratio of perimeters equals the _________

  39. For similar polygons, the ratio of perimeters equals the scale factor

  40. Complete for similar polygons/circles: Scale Factor = 2 : 3 Perimeter/Circumference Ratio = _____ Area Ratio = _____

  41. Perimeter Ratio = 2 : 3Area Ratio = 4 : 9 (22 : 32)

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