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I don't know what I am supposed to do. Please, help Problem: Similarity of noncongruent triangles is not possible in hyperbolic geometry. Where is the Euclidean parallel assumption used in the proof of the basic proportionality theorem? There are 2 parts, one is about hyperbolic geometry and other is about Euclidean parallel. In hyperbolic, Euclidean parallel is not applied. Hence I don't see relation between 2 parts on the problem. Appreciate any tips.

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