Locus: Equidistant from
Two Intersecting Lines

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A locus is a set of points which satisfies a certain condition.

theorem Locus Theorem 6
The locus equidistant from two intersecting lines, m1 and m2, is the pair of lines which bisect the angles formed by lines m1 and m2.

This theorem asks you to "describe the path formed by all points located the same distance for 2 intersecting lines".
ANSWER: a pair of lines which bisect the angles formed
Example 1: A park is designing a small Ferris wheel ride for young children. They currently have four condoles (seats) on the ride and wish to add four more. There are two supports rods (in blue) attached to the current condoles, and two additional support rods are needed that will be equally spaced from the existing rods. A drawing shows the new support rods as the angel bisectors of the intersection of the current rods.
Set of points: location of new support rods
Condition: equidistant from current rods
Locus: angle bisectors of current intersecting rods

Example 2: A city decides to place support poles equally spaced from two intersecting roads. The roads are straight lines surrounding this intersection. The possible placement of the poles are shown at the right. The poles lie on the angle bisectors of the intersecting roads.

Set of points: possible pole locations
Condition: equidistant from 2 lines
Locus: angle bisectors of intersecting roads



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