Theorem Homothety is a similarity transformation.
Evidence. Let O be the center of a homothety, k be the coefficient of a homothety, A and B be two arbitrary points of the figure.
With homothety, points A and B go to points A` and B` on the rays OA and OB, respectively, and OA` = k * OA, OB` = k * OB. Consequently
Then subtracting the equality term by term, we get:
Because
Thats
Therefore, homothety is a similarity transformation. The theorem is proved.
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