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7-2 Similar Polygons

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7-2 Similar Polygons. Similarity. Similar figures have the same shape but not necessarily the same size. The ~ symbol means “is similar to”

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similarity
Similarity
  • Similar figures have the same shape but not necessarily the same size.
    • The ~ symbol means “is similar to”
  • Two polygons are similar polygons if corresponding angles are congruent and if the lengths of corresponding sides are proportional.
  • When three or more ratios are equal, you can write an extended proportion.
understanding similarity
Understanding Similarity

MNP ~ SRT

  • What are the pairs of congruent angles?
  • What is the extended proportion for the ratios of corresponding sides?
defg hjkl
DEFG ~ HJKL
  • What are the pairs of congruent angles?
  • What is the extended proportion for the ratios of the lengths of corresponding sides?
scale factor
Scale Factor
  • A scale factor is the ratio of corresponding linear measurements of two similar figures.
    • The ratio of corresponding sides is , so the scale factor of ABC to XYZ is or 5 : 2.
determining similarity
Determining Similarity
  • Are the polygons similar? If they are, write a similarity statement and give the scale factor.
are the polygons similar if they are write a similarity statement and give the scale factor
 Are the polygons similar? If they are, write a similarity statement and give the scale factor.
using similar polygons
Using Similar Polygons
  • ABCD ~ EFGD. What is the value of x?

 What is the value of y?

using similarity
Using Similarity
  • In the diagram, Find SR.
scales
Scales
  • In a scale drawing, all lengths are proportional to their corresponding actual lengths.
  • The scale is the ratio that compares each length in the scale drawing to the actual length.
    • The lengths used in a scale can be in different units (ex. 1 cm = 50 km).
  • You can use proportions to find the actual dimensions represented in a scale drawing.
using a scale drawing
Using a Scale Drawing
  • The diagram shows a scale drawing of the Golden Gate Bridge. If the length between the two towers in the diagram is 6.4 cm, what is the length of the actual bridge?

If the tower measures 0.8 cm in the diagram, what is the actual height of the tower?

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