Similar Figures

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.

The areas of similar surfaces A₁ and A₂ have the same ratio as the squares of any two corresponding lines x₁ and x₂.

The volumes of similar solids V₁ and V₂ have the same ratio as the cubes of two corresponding lines x₁ and x₂.

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.