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Supplies:
colored paper, compass, ruler,
protractor
Directions: Have
the students connect their understanding of constructions with their
knowledge of loci.
For Theorems 2, 3, and 4, the exploration
is a simple investigation of the basic theorems. For Theorem 5,
the exploration may be applied to several scenarios.
Example Theorem 2: Have students
draw a straight line. Utilizing construction, draw the locus of points
equidistant from the line.
Example Theorem 3: Have students locate two
points on their papers. Utilizing construction, draw the locus of
points equidistant from the two points. The ruler can be used to
verify that the lengths are equal.
Example Theorem 4: Have students construct two
parallel lines. Utilizing construction, draw the locus of points
equidistant from two parallel lines.
Example Theorem 5: Have students prepare the
following using a straightedge and/or compass:
1. an acute angle of
any size
2. an obtuse angle of any size
3. a right angle (produced through construction)
4. two intersecting lines
5. two intersecting lines which are perpendicular (produced through
construction)
Students will locate the
locus of points equidistant from the sides of the angles and the two
intersecting lines. The loci will to be constructed using the
compass. The protractor is to be used to verify that the
constructions produced angle bisectors.
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