CK12 - Geometry

Lookat the diagrambelow. We can makea corollaryto the previoustheorem.

are labelsfor lines

are lengthsof segments

are parallelbut not equallyspaced

We’re giventhat lines , , and are parallel.We can see that the parallellinescut lines and
(transversals).A corollaryto the TriangleProportionalityTheoremstatesthat the segmentlengthson one
transversalare proportionalto the segmentlengthson the othertransversal.

Conclusion: and

Example 4

The corollaryin example3 can be broadenedtoanynumberof parallellinesthat cutanynumberof
transversals.Whenthis happens,allcorrespondingsegmentsof the transversalsare proportional!

The diagrambelowshowsseveralparallellines, , , and , that cut severaltransversals ,

, and.