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Similar Polygons

Similar Polygons. Informal Definition of Similar Figures. Two figures are similar if they have the same shape. (They do not necessarily have the same size.). B. C. D. F. E. A. Formal Definition of Similar Polygons.

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Similar Polygons

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  1. Similar Polygons

  2. Informal Definition of Similar Figures Two figures are similar if they have the same shape. (They do not necessarily have the same size.)

  3. B C D F E A Formal Definition of Similar Polygons Two polygons are similar iff their corresponding angles are congruent,and (lengths of) corresponding sides are proportional. •  A  D •  B  E •  C  F

  4. B 10 C 7 Y X 5 14 18 9 Z A Proportional (Lengths of) sides are proportionaliff ratios of (lengths of) corresponding sides are equal. For example: so the sides are proportional.

  5. B 10 C 5 Y X 7 14 18 9 Z A Scale Factor The ratio of corresponding sides of similar polygons. ExampleThe scale factor • from ABC to _____ is____. • from ZYXto ABC is____. ZYX 2 1/2

  6. Naming Similar Polygons **Must match the corresponding letters**

  7. Applying the Definition - Angles **Must match the corresponding vertices**

  8. Applying the Definition - Sides **Must match the corresponding sides** Proportional means all of the ratios are equal!

  9. 14 8 18 24 28 Given Find the lengths of the missing sides. Example 1

  10. 14 8 18 24 28 Given Find AC Example 1 Step 1: Write out a proportion of for the sides. (Be sure to match up corresponding letters!)

  11. 14 8 18 24 28 Given Find the lengths of the missing sides. Example 1 Step 2: Replace the sides with the lengths from the problem.

  12. 14 8 18 24 28 Given Find the lengths of the missing sides. Example 1 Step 3: Cross-multiply and solve.

  13. 14 8 18 24 28 Given Example 1 You should be able to find CD and BD as well!

  14. 14 8 18 24 28 The scale factor of ABDC to RPSQ is Given Find the scale factor of ABDC to RPSQ Example 2 Remember the scale factor is same as the ratio of the sides. Always put the first polygon mentioned in the numerator.

  15. A 15 E D x H 20 y 10 5 F B z G C 30 Example 3 ABCD  EFGH. Solve for x, y and z. Step 1: Write a proportion using names of sides. Step 2: Substitute values. Step 3: Cross-multiply to solve. Step 4: Repeat to find other values. y = 10 z = 15 x = 7.5

  16. Dilations and Scale Factor A dilation is a transformation that changes the size of an object. The scale factor is the ratio of the lengths of the corresponding sides of two similar polygons. It indicates the relative size of one polygon compared the another.

  17. Congruent Triangles • Are congruent triangles similar? • What is the scale factor between two congruent triangles?

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