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If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on any other transversal.

Answer :

Final answer:

Parallel lines cut off congruent segments on any transversal due to the properties of Euclidean geometry.

Explanation:

If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on any transversal. This conclusion follows from the properties of parallel lines and transversals in Euclidean geometry. When a set of parallel lines intersects a transversal, the corresponding angles formed are congruent, and the intercepted segments between the lines on the transversal are also congruent.

As per the principles of geometry, especially those concerning parallel lines and transversals, if one transversal intersects parallel lines and creates congruent segments, then every transversal crossing these lines will create segments of equal length. This is because lines parallel to the same line are also parallel to each other, preserving the distances between them across the plane.

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