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Assume that all distances are measured along the appropriate perpendicular. There is no specific name for the locus since the locus can be two or one straight lines, depending upon the original two lines.

If the two lines are intersecting then the locus is a pair of straight lines that bisect the two angles formed by the original lines.

If the original two lines are parallel, then the locus is a line parallel to them and halfway between them.

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