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Exploring the Locus of Points Relative to Parallel and Intersecting Lines in Geometry

This lesson introduces students to the concept of loci in relation to parallel and intersecting lines. Key objectives include understanding how to identify the locus of points that are equidistant from two parallel lines and those equidistant from intersecting lines. The Locus Theorem states that the locus of points equidistant from two parallel lines is a line midway between them, while the locus from intersecting lines consists of two angle bisectors. Practice examples help reinforce these concepts and encourage practical application.

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Exploring the Locus of Points Relative to Parallel and Intersecting Lines in Geometry

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  1. Think About It!! Describe the locus of points a distance of 2 from a line segment of length 5.

  2. Locus of 2 Parallel Lines and Locus of 2 Intersecting Lines Geometry Unit 7, Day 4 Ms. Reed

  3. Objective: • To learn how to find the locus of two parallel lines • To learn how to find the locus of two intersecting lines

  4. Locus Theorem 4: • The locus of points equidistant from two parallel lines, l1 and l2 , is a line parallel to both l1 and  l2 and midway between them.

  5. Practice: • During your morning jog, you run down an alley between two buildings which are parallel to one another and are 20 feet apart.  Describe your path through the alley so that you are always the same distance from both buildings. • You run parallel to the buildings, 10 feet from each.

  6. More Practice: • http://www.regentsprep.org/Regents/math/geometry/GL1/PracLoc4.htm

  7. Locus Theorem 5: • The locus of points equidistant from two intersecting lines, l1 and l2, is a pair of bisectors that bisect the angles formed by l1 and l2 .

  8. Practice • http://www.regentsprep.org/Regents/math/geometry/GL1/PracLoc5.htm

  9. Homework • Work Packets: Locus of 2 Parallel Lines, Locus of 2 Intersecting Lines

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