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Understanding Similar Polygons and Scale Factor

Learn about how similar polygons are smaller versions of each other and how to find the scale factor to compare their corresponding sides. Examine corresponding angles and sides in these polygonal shapes.

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Understanding Similar Polygons and Scale Factor

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  1. Similar Polygons Spi.2.2.B Section 6-2 Circle Limit III M.C. Escher Jim Smith JCHS

  2. Similar figures look alike but one is a smaller version of the other. Like Dr. Evil and Mini-Me. It wouldn’t make much sense to make a drawing of this ship the actual size of the ship.

  3. Just like congruent polygons, the corresponding angles in similar polygons must be congruent.

  4. A = 80° B = 30° Z = 170° W = ___ X = ___ D = ___ 80° 30° 170° B A W X Z Y D C

  5. The sides are a little different. They must be PROPORTIONAL. AB = BC = CD = DA WX XY YZ ZW B A W X Z Y D C

  6. This means I should be able to multiply each side of the smaller polygon by the same number and get it’s corresponding side on the bigger polygon. 4x2 = 8 4 3x2 = 6 5x2 = 10 3 5 2 2x2 = 4

  7. The SCALE FACTOR is the ratio of the corresponding sides SMALLBIG BIG SMALL or

  8. What is the scale factor of these polygons? 10 4 6 X 7 Z Y 8 10 4 5 2 = Scale Factor =

  9. 10 4 5 2 56 2 Z = = Use the scale factor to find the other sides 10 4 7 Z 6 X SF = Y 8 5X 2 7 58 2 Y = = 5y = 16 y = 16 = 3.2 5 5z = 12 z = 12 = 2.4 5 2x = 35 x = 35 = 17.5 2

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