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Bevis

Bevis för transversalsatsen

En parallelltransversal inritad i en triangel delar, enligt transversalsatsen, två av triangelns sidor så att
där avstånden ges av figuren nedan.
Transversalsatsen proof 1.svg
Enligt topptriangelsatsen gäller
dvs. kvoten mellan en sidlängd i den stora triangeln och motsvarande sidlängd i topptriangeln är konstant.
a(c+d)=c(a+b)
ac+ad=ac+cb
ad=cb

Detta är transversalsatsen.

Q.E.D.

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