Similar Figures
Two surfaces or solids are similar if any two corresponding sides or planes are proportional.
![Example of similar figures: spheres, cylinders, and regular hexagons](/sites/default/files/images/similar-figures.jpg)
In similar figures of any kind, pairs of corresponding line segments such as x1, x2 and y1, y2 have the same ratio.
$\dfrac{x_1}{x_2} = \dfrac{y_1}{y_2}$
The areas of similar surfaces A1 and A2 have the same ratio as the squares of any two corresponding lines x1 and x2.
$\dfrac{A_1}{A_2} = \dfrac{{x_1}^2}{{x_2}^2}$
The volumes of similar solids V1 and V2 have the same ratio as the cubes of two corresponding lines x1 and x2.
$\dfrac{V_1}{V_2} = \dfrac{{x_1}^3}{{x_2}^3}$
Some Facts About Similar Figures
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- Regular polygons of the same kind are all similar.
- All circles are similar.
- All squares are similar.
- All equilateral triangles are similar.
- Two isosceles triangles are only similar if they have equal vertex angle.
- Right circular cones are similar if they have equal vertex angle.
- If the central angle of two circular sectors are equal, they are similar.
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