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fundamental theorem of similarity
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Fundamental theorem of similarity Projective version of the fundamental theorem of similarityIn RP, Euclid's fundamental theorem of similarity states that CD/DA = CE/EB. By introducing a scaling factor, the theorem can be saved in RP as Cā€²Dā€²/Dā€²Aā€² = Cā€²Eā€²/Eā€²Bā€² āˆ™ Ī©Bā€²/Ī©Aā€². Note that while lines AB and DE are parallel in RP, their projections onto PP intersect at the infinitely distant horizon (Ī©).
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fundamental theorem of similarity

mathematics
Also known as: proportional segments theorem
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Fundamental theorem of similarity
Fundamental theorem of similarity The formula in this diagram reads k is to l as m is to n if and only if line DE is parallel to line AB. This theorem then enables one to show that the small and large triangles are similar.

The fundamental theorem of similarity, also known as the proportional segments theorem, states that a line segment drawn through a triangle, parallel to one of its sides, divides the other two sides proportionally[1

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4 Britannica Sources
  1. side-angle-side theorem
  2. projective geometry
  3. Euclidean geometry
  4. triangle

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