In details

Polygon similarity properties


If two polygons are similar, then the ratio between their perimeters It is equal to the ratio between the two-sided measures of either polygon.

Demonstration:

Being A B C D ~ THE'B'Ç'D', We have to:

The perimeters of these polygons can be represented as follows:
Perimeter of ABCDE (2P) = AB + BC + CD + IN + AND THEPerimeter of THE'B'Ç'D'E' (2P') = THE'B' + B'Ç' + Ç'D' + D'AND' + AND'THE'

By a property of proportions, we can say that:

Example:

  • The sides of a triangle measure 3.6 cm, 6.4 cm and 8 cm. This triangle is similar to another whose perimeter measures 45 cm. Calculate the sides of the second triangle.
    Solution:
    Similarity ratio =


    Therefore, the sides of the second triangle are 9cm, 16cm and 20cm.

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