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Circle Limit III M.C. Escher

Similar Polygons. Circle Limit III M.C. Escher. Figures that are similar (~) have the same shape but not necessarily the same size. Similar figures look alike but one is a smaller version of the other. It wouldn’t make much sense to make a drawing

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Circle Limit III M.C. Escher

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  1. Similar Polygons Circle Limit III M.C. Escher

  2. Figures that are similar(~) have the same shape but not necessarily the same size.

  3. Similar figures look alike but one is a smaller version of the other. It wouldn’t make much sense to make a drawing of this ship the actual size of the ship.

  4. Two polygons are similar polygons if and only if their corresponding angles are congruent & their corresponding side lengths are proportional. All the angles are the same All sides are proportional

  5. Similar Polygons – 2 polygons that have the same shape but not the same size. • Symbol ( ~ ) • Corresponding s are . • Corresponding sides are Proportional. Equal Ratios: ** Reduce to the same fraction!!

  6. Writing Math Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order.

  7. Ex: Order Matters Y • ΔABC ~ ΔXYZ 78 4 6 BC corresponds to YZ B 42 Z X 8 10 Find AB: 4 6 = AB = 15 10 AB A C 4 8 = AC = 20 mB = mC = 78 60 10 AC Find AC:

  8. Example : Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. rectangles ABCD and EFGH

  9. Example 3 A boxcar has the dimensions shown. A model of the boxcar is 1.25 in. wide. Find the length of the model to the nearest inch.

  10. Example 3 Continued 1.25(36.25) = x(9) Cross Products Prop. 45.3 = 9x Simplify. 5 x Divide both sides by 9. The length of the model is approximately 5 inches.

  11. Ex. 2: Are the following polygons similar? 2in B C 120 1in K L 1in 4in 4in 2in 2in 80 J M 1in A D 2in • Check to see if all s are ? • Check the ratio of all corresponding sides?

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