Let's have the triangle ABC and the points M, N ∈(BC). If
then this relation is true:
We use small geometric constructions. We build BE || AC, E ∈AM and CF || AB, F ∈ AN.
(angles with parallel sides) (1)
(we know this from the hypothesys) (2)
From (1) and (2) we have,
BE || AC => (acc. Fundamental Theorem of Similarity)
CF || AB => (acc. Fundamental Theorem of Similarity)
From the last two relations we get:
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