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Geometric Similarity Theorems & Proportions in Polygons

Learn about the properties of similar polygons and theorems related to their proportions. Understand the Cross Product Property, Geometric Mean, and Triangle Similarity Postulates. Discover ways to show triangles are similar and apply proportionality theorems. Master the SAS and SSS Similarity Theorems for triangles.

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Geometric Similarity Theorems & Proportions in Polygons

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  1. The product of the means equals the product of the extremes Cross product property

  2. It is the square root of the product. Geometric mean

  3. The corresponding angles are congruent. The corresponding sides are proportional Similar polygons

  4. If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths. This is the scale factor. Perimeters of similar polygons

  5. If two polygons are similar, then the ratio of any two corresponding lengths in the polygon is equal to the scale factor of the similar polygons. Corresponding lengths in similar polygons

  6. AA (Angle – Angle) Similarity Postulate SSS (Side – Side – Side) Similarity Theorem SAS (Side – Angle – Side) Similarity Theorem Ways to show triangles are similar

  7. If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. Triangle proportionality theorem

  8. If a line divides two sides of a triangle proportionally, then it is parallel to the third side. Converse of the triangle proportionality theorem

  9. If three parallel lines intersect two transversals, then they divide the transversals proportionally Theorem 6.6

  10. If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. Theorem 6.7

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