Two surfaces or solids are similar if any two corresponding sides or planes are proportional.

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.

$\dfrac{V_1}{V_2} = \dfrac{{x_1}^3}{{x_2}^3}$

• 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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